Edit Profile (opens in new tab) Song, Renming Co-Author Distance Author ID: song.renming Published as: Song, Renming; Song, R.; Song, Ren Ming; Song, RenMing more...less Further Spellings: 宋仁明 Homepage: http://www.math.uiuc.edu/~rsong/ External Links: MGP · ORCID · Wikidata · Google Scholar · ResearchGate · dblp · GND · IdRef Documents Indexed: 184 Publications since 1984, including 2 Books and 18 Additional arXiv Preprints 2 Contributions as Editor Reviewing Activity: 115 Reviews Co-Authors: 70 Co-Authors with 176 Joint Publications 2,017 Co-Co-Authors all top 5 Co-Authors 10 single-authored 57 Kim, Panki 47 Vondraček, Zoran 41 Ren, Yanxia 30 Chen, Zhen-Qing 14 Zhang, Rui 9 Hou, Haojie 8 Rao, Murali 7 Glover, Joseph 7 Sun, Zhenyao 6 Liu, Rongli 5 Cho, Soobin 5 Duan, Jinqiao 5 Hu, Ze-Chun 5 Park, Hyunchul 5 Šikić, Hrvoje 5 Xie, Longjie 3 Ma, Zhi-Ming 3 Wu, Peixue 2 Bo, Lijun 2 Conlon, Joseph G. 2 Hao, Chenxu 2 Huang, Qiao 2 Li, Xiaofan 2 Ma, Ting 2 Schilling, René Leander 2 Tan, Yuan 2 Tang, Dan 2 Wang, Hong 2 Wang, Yongjin 2 Xiao, Yimin 2 Xie, Yingchao 2 Yang, Xuewei 2 Yang, Zhiwei 2 Zhao, Jianjie 1 Burkholder, Donald L. 1 Chen, Ao 1 Chen, Peng 1 Davis, Burgess 1 Engländer, János 1 Feng, Liming 1 Fitzsimmons, Patrick J. 1 Gao, Ting 1 Grzywny, Tomasz 1 Hao, Mengli 1 Herrell, Randall 1 Jiang, Yiyang 1 Kinzebulatov, Damir 1 Kyprianou, Andreas E. 1 Li, Shoumei 1 Li, Zhichan 1 Liu, Wei 1 Olsen, Peder A. 1 Peng, Xue 1 Pop-Stojanovic, Zoran R. 1 Rivero, Víctor Manuel 1 Semënov, Yuliy A. 1 Sowers, Richard B. 1 Wang, Hao 1 Wang, Xiao 1 Wu, Dongsheng 1 Wu, Jang-Mei 1 Wu, Shukun 1 Xu, Wei 1 Yang, Ting 1 Yang, Xiaochuan 1 Zhang, Junfei 1 Zhang, Xicheng 1 Zhao, Han 1 Zhou, Qianqian 1 Zhou, Xianyin 1 Zhu, Yaping all top 5 Serials 17 Stochastic Processes and their Applications 11 Potential Analysis 9 Journal of Functional Analysis 9 Probability Theory and Related Fields 8 Journal of Theoretical Probability 7 Electronic Journal of Probability 6 Illinois Journal of Mathematics 5 The Annals of Probability 5 Science China. Mathematics 4 Transactions of the American Mathematical Society 4 Acta Applicandae Mathematicae 4 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 4 Electronic Communications in Probability 3 Journal of Mathematical Analysis and Applications 3 Journal of Applied Probability 3 Journal of Differential Equations 3 Mathematische Annalen 3 Mathematische Zeitschrift 3 Tôhoku Mathematical Journal. Second Series 3 Acta Mathematicae Applicatae Sinica. English Series 3 Forum Mathematicum 2 Advances in Applied Probability 2 Journal of Statistical Physics 2 Mathematische Nachrichten 2 Proceedings of the London Mathematical Society. Third Series 2 Insurance Mathematics & Economics 2 Fuzzy Mathematics 2 Revista Matemática Iberoamericana 2 Glasnik Matematički. Serija III 2 Journal of the European Mathematical Society (JEMS) 2 De Gruyter Studies in Mathematics 1 Rocky Mountain Journal of Mathematics 1 Annales de l’Institut Fourier 1 Applied Mathematics and Computation 1 Bulletin of the London Mathematical Society 1 Control and Cybernetics 1 Journal of the Korean Mathematical Society 1 Journal of the London Mathematical Society. Second Series 1 Journal für die Reine und Angewandte Mathematik 1 Osaka Journal of Mathematics 1 Statistics & Probability Letters 1 Bulletin pour les Sous Ensembles Flous et Leurs Applications 1 Stochastic Analysis and Applications 1 Chinese Journal of Applied Probability and Statistics 1 Applied Mathematical Modelling 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Scientific Computing 1 Bernoulli 1 Acta Mathematica Sinica. English Series 1 ALEA. Latin American Journal of Probability and Mathematical Statistics 1 Frontiers of Mathematics in China 1 Scientia Sinica. Mathematica 1 Advances in Nonlinear Analysis all top 5 Fields 161 Probability theory and stochastic processes (60-XX) 31 Potential theory (31-XX) 28 Operator theory (47-XX) 22 Partial differential equations (35-XX) 4 Measure and integration (28-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 History and biography (01-XX) 2 Special functions (33-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Statistics (62-XX) 2 Numerical analysis (65-XX) 2 Biology and other natural sciences (92-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Quantum theory (81-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 146 Publications have been cited 3,075 times in 1,668 Documents Cited by ▼ Year ▼ Bernstein functions. Theory and applications. 2nd revised and extended ed. Zbl 1257.33001 Schilling, René L.; Song, Renming; Vondraček, Zoran 377 2012 Bernstein functions. Theory and applications. Zbl 1197.33002 Schilling, René L.; Song, Renming; Vondraček, Zoran 236 2010 Estimates on Green functions and Poisson kernels for symmetric stable processes. Zbl 0918.60068 Chen, Zhen-Qing; Song, Renming 132 1998 Heat kernel estimates for the Dirichlet fractional Laplacian. Zbl 1203.60114 Chen, Zhen-Qing; Kim, Panki; Song, Renming 122 2010 Two-sided eigenvalue estimates for subordinate processes in domains. Zbl 1081.60056 Chen, Zhen-Qing; Song, Renming 84 2005 Potential theory of subordinate killed Brownian motion in a domain. Zbl 1022.60078 Song, Renming; Vondraček, Zoran 64 2003 Intrinsic ultracontractivity and conditional gauge for symmetric stable processes. Zbl 0886.60072 Chen, Zhen-Qing; Song, Renming 64 1997 Mean exit time and escape probability for dynamical systems driven by Lévy noises. Zbl 1318.60065 Gao, T.; Duan, J.; Li, X.; Song, R. 59 2014 Drift transforms and Green function estimates for discontinuous processes. Zbl 1031.60071 Chen, Zhen-Qing; Song, Renming 58 2003 Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation. Zbl 1264.60060 Chen, Zhen-Qing; Kim, Panki; Song, Renming 57 2012 Harnack inequality for some classes of Markov processes. Zbl 1052.60064 Song, Renming; Vondraček, Zoran 56 2004 Boundary Harnack principle for symmetric stable processes. Zbl 0945.31006 Song, Renming; Wu, Jang-Mei 53 1999 Two-sided heat kernel estimates for censored stable-like processes. Zbl 1190.60068 Chen, Zhen-Qing; Kim, Panki; Song, Renming 50 2010 Boundary Harnack principle for \(\Delta +\Delta ^{\alpha /2}\). Zbl 1271.31006 Chen, Zhen-Qing; Kim, Panki; Song, Renming; Vondraček, Zoran 47 2012 Global uniform boundary Harnack principle with explicit decay rate and its application. Zbl 1296.60198 Kim, Panki; Song, Renming; Vondraček, Zoran 47 2014 Sharp heat kernel estimates for relativistic stable processes in open sets. Zbl 1235.60101 Chen, Zhen-Qing; Kim, Panki; Song, Renming 42 2012 Green function estimates and Harnack inequality for subordinate Brownian motions. Zbl 1107.60042 Rao, Murali; Song, Renming; Vondraček, Zoran 40 2006 Conditional gauge theorem for non-local Feynman-Kac transforms. Zbl 1025.60032 Chen, Zhen-Qing; Song, Renming 40 2003 General gauge and conditional gauge theorems. Zbl 1017.60086 Chen, Zhen-Qing; Song, Renming 40 2002 Potential theory of subordinate Brownian motions revisited. Zbl 1282.60076 Kim, Panki; Song, Renming; Vondraček, Zoran 39 2012 Martin boundary and integral representation for harmonic functions of symmetric stable processes. Zbl 0954.60003 Chen, Zhen-Qing; Song, Renming 36 1998 Dirichlet heat kernel estimates for rotationally symmetric Lévy processes. Zbl 1304.60080 Chen, Zhen-Qing; Kim, Panki; Song, Renming 36 2014 Hardy inequality for censored stable processes. Zbl 1070.46021 Chen, Zhen-Qing; Song, Renming 35 2003 Two-sided estimates on the density of Brownian motion with singular drift. Zbl 1110.60071 Kim, Panki; Song, Renming 34 2006 Dirichlet heat kernel estimates for \(\Delta ^{\alpha /2} + \delta ^{\beta /2}\). Zbl 1268.60101 Chen, Zhen-Qing; Kim, Panki; Song, Renming 33 2010 Two-sided Green function estimates for killed subordinate Brownian motions. Zbl 1248.60091 Kim, Panki; Song, Renming; Vondraček, Zoran 33 2012 Boundary Harnack principle for subordinate Brownian motions. Zbl 1166.60046 Kim, Panki; Song, Renming; Vondraček, Zoran 29 2009 Convexity and smoothness of scale functions and de Finetti’s control problem. Zbl 1188.93115 Kyprianou, Andreas E.; Rivero, Víctor; Song, Renming 28 2010 Potential theory of geometric stable processes. Zbl 1099.60051 Šikić, Hrvoje; Song, Renming; Vondraček, Zoran 27 2006 Heat kernel estimates for \(\Delta +\Delta ^{\alpha /2}\) in \(C^{1, 1}\) open sets. Zbl 1229.60089 Chen, Zhen-Qing; Kim, Panki; Song, Renming 27 2011 Heat kernels of non-symmetric jump processes: beyond the stable case. Zbl 1409.60116 Kim, Panki; Song, Renming; Vondraček, Zoran 25 2018 Intrinsic ultracontractivity of non-symmetric diffusion semigroups in bounded domains. Zbl 1167.60017 Kim, Panki; Song, Renming 25 2008 Stochastic flows for Lévy processes with Hölder drifts. Zbl 1420.60064 Chen, Zhen-Qing; Song, Renming; Zhang, Xicheng 25 2018 Intrinsic ultracontractivity, conditional lifetimes and conditional gauge for symmetric stable processes on rough domains. Zbl 0959.60035 Chen, Zhen-Qing; Song, Renming 24 2000 Potential theory of truncated stable processes. Zbl 1115.60073 Kim, Panki; Song, Renming 24 2007 Uniform boundary Harnack principle for rotationally symmetric Lévy processes in general open sets. Zbl 1262.60077 Kim, Panki; Song, RenMing; Vondraček, Zoran 23 2012 Potential theory of subordinate Brownian motion. Zbl 1203.60118 Song, R.; Vondraček, Z. 23 2009 Potential theory of special subordinators and subordinate killed stable processes. Zbl 1119.60063 Song, Renming; Vondraček, Zoran 23 2006 On the relationship between subordinate killed and killed subordinate processes. Zbl 1187.60057 Song, Renming; Vondracek, Zoran 22 2008 A remark on diffusion of directed polymers in random environments. Zbl 0924.60053 Song, Renming; Zhou, Xian Yin 22 1996 Stable process with singular drift. Zbl 1336.60112 Kim, Panki; Song, Renming 22 2014 Factorization and estimates of Dirichlet heat kernels for non-local operators with critical killings. Zbl 1460.60087 Cho, Soobin; Kim, Panki; Song, Renming; Vondraček, Zoran 22 2020 Quasi-stationarity and quasi-ergodicity of general Markov processes. Zbl 1309.60078 Zhang, Junfei; Li, Shoumei; Song, Renming 20 2014 \(L \log L\) criterion for a class of superdiffusions. Zbl 1175.60077 Liu, Rong-Li; Ren, Yan-Xia; Song, Renming 20 2009 Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation. Zbl 1321.60149 Chen, Zhen-Qing; Kim, Panki; Song, Renming 20 2015 Global heat kernel estimate for relativistic stable processes in exterior open sets. Zbl 1255.60076 Chen, Zhen-Qing; Kim, Panki; Song, Renming 19 2012 Potential theory of subordinate Brownian motions with Gaussian components. Zbl 1266.31007 Kim, Panki; Song, Renming; Vondraček, Zoran 19 2013 Strong law of large numbers for a class of superdiffusions. Zbl 1260.60170 Liu, Rong-Li; Ren, Yan-Xia; Song, Renming 18 2013 Estimates on the Dirichlet heat kernel of domains above the graphs of bounded \(C^{1,1}\) functions. Zbl 1064.35066 Song, Renming 18 2004 Sharp Green function estimates for \(\Delta + \delta ^{\alpha /2}\) in \(C^{1,1}\) open sets and their applications. Zbl 1257.31002 Chen, Zhen-Qing; Kim, Panki; Song, Renming; Vondraček, Zoran 17 2010 Parabolic Harnack inequality for the mixture of Brownian motion and stable process. Zbl 1143.60049 Song, Renming; Vondraček, Zoran 17 2007 Dirichlet heat kernel estimates for subordinate Brownian motions with Gaussian components. Zbl 1333.60179 Chen, Zhen-Qing; Kim, Panki; Song, Renming 17 2016 Central limit theorems for supercritical branching nonsymmetric Markov processes. Zbl 1365.60020 Ren, Yan-Xia; Song, Renming; Zhang, Rui 16 2017 Sharp bounds on the density, Green function and jumping function of subordinate killed BM. Zbl 1054.60080 Song, Renming 16 2004 Intrinsic ultracontractivity for non-symmetric Lévy processes. Zbl 1175.47040 Kim, Panki; Song, Renming 15 2009 Estimates on Green functions and Schrödinger-type equations for non-symmetric diffusions with measure-valued drifts. Zbl 1118.35007 Kim, Panki; Song, Renming 14 2007 Two-sided estimates on the density of the Feynman-Kac semigroups of stable-like processes. Zbl 1112.60059 Song, Renming 14 2006 Intrinsic ultracontractivity of nonsymmetric diffusions with measure-valued drifts and potentials. Zbl 1175.47039 Kim, Panki; Song, Renming 13 2008 Potential theory of subordinate killed Brownian motion. Zbl 1450.60040 Kim, Panki; Song, Renming; Vondraček, Zoran 13 2019 Asymmetric non-Gaussian effects in a tumor growth model with immunization. Zbl 1428.92049 Hao, Mengli; Duan, Jinqiao; Song, Renming; Xu, Wei 13 2014 Boundary behavior of harmonic functions for truncated stable processes. Zbl 1145.60026 Kim, Panki; Song, Renming 12 2008 Harnack inequality for some discontinuous Markov processes with a diffusion part. Zbl 1075.60096 Song, Renming; Vondraček, Zoran 12 2005 Central limit theorems for supercritical branching Markov processes. Zbl 1292.60034 Ren, Yan-Xia; Song, Renming; Zhang, Rui 12 2014 Quadratic forms corresponding to the generalized Schrödinger semigroups. Zbl 0807.60056 Glover, J.; Rao, M.; Šikić, H.; Song, R. 12 1994 Continuity of eigenvalues of subordinate processes in domains. Zbl 1090.60070 Chen, Zhen-Qing; Song, Renming 12 2006 Global heat kernel estimates for relativistic stable processes in half-space-like open sets. Zbl 1239.60076 Chen, Zhen-Qing; Kim, Panki; Song, Renming 12 2012 On suprema of Lévy processes and application in risk theory. Zbl 1178.60036 Song, Renming; Vondraček, Zoran 11 2008 Lévy risk model with two-sided jumps and a barrier dividend strategy. Zbl 1244.91044 Bo, Lijun; Song, Renming; Tang, Dan; Wang, Yongjin; Yang, Xuewei 11 2012 On dual processes of non-symmetric diffusions with measure-valued drifts. Zbl 1146.60060 Kim, Panki; Song, Renming 10 2008 Spectral heat content for Lévy processes. Zbl 1472.35209 Grzywny, Tomasz; Park, Hyunchul; Song, Renming 10 2019 A 2-spine decomposition of the critical Galton-Watson tree and a probabilistic proof of Yaglom’s theorem. Zbl 1394.60089 Ren, Yan-Xia; Song, Renming; Sun, Zhenyao 10 2018 Sharp space-time regularity of the solution to stochastic heat equation driven by fractional-colored noise. Zbl 1447.60064 Herrell, Randall; Song, Renming; Wu, Dongsheng; Xiao, Yimin 10 2020 Central limit theorems for supercritical superprocesses. Zbl 1325.60019 Ren, Yan-Xia; Song, Renming; Zhang, Rui 9 2015 Limit theorems for some critical superprocesses. Zbl 1338.60074 Ren, Yan-Xia; Song, Renming; Zhang, Rui 9 2015 Martin boundary for some symmetric Lévy processes. Zbl 1336.31031 Kim, Panki; Song, Renming; Vondraček, Zoran 9 2015 Scale invariant boundary Harnack principle at infinity for Feller processes. Zbl 1381.60110 Kim, Panki; Song, Renming; Vondraček, Zoran 9 2017 Feynman-Kac semigroup with discontinuous additive functionals. Zbl 0831.60085 Song, Renming 9 1995 Application of Carleson’s theorem to wavelet inversion. Zbl 0816.42018 Rao, Murali; Šikić, Hrvoje; Song, Renming 9 1994 The extremal process of super-Brownian motion. Zbl 1469.60260 Ren, Yan-Xia; Song, Renming; Zhang, Rui 9 2021 On the boundary theory of subordinate killed Lévy processes. Zbl 1451.60090 Kim, Panki; Song, Renming; Vondraček, Zoran 9 2020 On the (N) fuzzy integral. Zbl 0641.28014 Song, Renming 8 1985 Boundary Harnack principle for Brownian motions with measure-valued drifts in bounded Lipschitz domains. Zbl 1140.60038 Kim, Panki; Song, Renming 8 2007 Central limit theorems for super Ornstein-Uhlenbeck processes. Zbl 1301.60027 Ren, Yan-Xia; Song, Renming; Zhang, Rui 8 2014 Strong law of large numbers for supercritical superprocesses under second moment condition. Zbl 1332.60044 Chen, Zhen-Qing; Ren, Yan-Xia; Song, Renming; Zhang, Rui 8 2015 Probabilistic approach to the Dirichlet problem of perturbed stable processes. Zbl 0792.60067 Song, Renming 8 1993 Small time asymptotics of spectral heat contents for subordinate killed Brownian motions related to isotropic \({\alpha}\)-stable processes. Zbl 1481.60165 Park, Hyunchul; Song, Renming 8 2019 Green function estimates for relativistic stable processes in half-space-like open sets. Zbl 1235.60100 Chen, Zhen-Qing; Kim, Panki; Song, Renming 8 2011 \(L \log L\) condition for supercritical branching Hunt processes. Zbl 1215.60050 Liu, Rong-Li; Ren, Yan-Xia; Song, Renming 7 2011 On the potential theory of one-dimensional subordinate Brownian motions with continuous components. Zbl 1202.60125 Kim, Panki; Song, Renming; Vondraček, Zoran 7 2010 Trace estimates for relativistic stable processes. Zbl 1308.60059 Park, Hyunchul; Song, Renming 7 2014 Accessibility, martin boundary and minimal thinness for Feller processes in metric measure spaces. Zbl 1395.60094 Kim, Panki; Song, Renming; Vondraček, Zoran 7 2018 Spine decompositions and limit theorems for a class of critical superprocesses. Zbl 1434.60250 Ren, Yan-Xia; Song, Renming; Sun, Zhenyao 7 2020 Dirichlet heat kernel estimates for stable processes with singular drift in unbounded \(C^{1,1}\) open sets. Zbl 1301.60088 Kim, Panki; Song, Renming 7 2014 Boundary Harnack principle and Martin boundary at infinity for subordinate Brownian motions. Zbl 1302.60110 Kim, Panki; Song, Renming; Vondraček, Zoran 7 2014 Diffusion of directed polymers in a strong random environment. Zbl 1081.82626 Olsen, Peder; Song, Renming 7 1996 Probabilistic methods in Schrödinger equations. Zbl 0691.60050 Ma, Zhiming; Song, Renming 6 1990 Stable central limit theorems for super Ornstein-Uhlenbeck processes. Zbl 1428.60120 Ren, Yan-Xia; Song, Renming; Sun, Zhenyao; Zhao, Jianjie 6 2019 Weak extinction versus global exponential growth of total mass for superdiffusions. Zbl 1341.60102 Engländer, János; Ren, Yan-Xia; Song, Renming 6 2016 Harmonic functions of subordinate killed Brownian motion. Zbl 1061.60077 Glover, J.; Pop-Stojanovic, Z.; Rao, M.; Šikić, H.; Song, R.; Vondraček, Z. 6 2004 Limit theorems for a class of critical superprocesses with stable branching. Zbl 1434.60235 Ren, Yan-Xia; Song, Renming; Sun, Zhenyao 6 2020 Stochastic transport equation with singular drift. Zbl 1537.35435 Kinzebulatov, Damir; Semënov, Yuliy A.; Song, Renming 2 2024 Homogenization of non-Symmetric jump processes. Zbl 1533.35018 Huang, Qiao; Duan, Jinqiao; Song, Renming 1 2024 On potential theory of Markov processes with jump kernels decaying at the boundary. Zbl 1508.60079 Kim, Panki; Song, Renming; Vondraček, Zoran 4 2023 Positive self-similar Markov processes obtained by resurrection. Zbl 1508.60048 Kim, Panki; Song, Renming; Vondraček, Zoran 2 2023 Weak and strong well-posedness of critical and supercritical SDEs with singular coefficients. Zbl 1532.60130 Song, Renming; Xie, Longjie 2 2023 Subcritical superprocesses conditioned on non-extinction. Zbl 1517.60108 Liu, Rongli; Ren, Yan-Xia; Song, Renming; Sun, Zhenyao 1 2023 Branching Brownian motion in a periodic environment and uniqueness of pulsating traveling waves. Zbl 1518.60083 Ren, Yan-Xia; Song, Renming; Yang, Fan 1 2023 Spectral heat content for \(\alpha \)-stable processes in \({C^{1,1}}\) open sets. Zbl 1486.60066 Park, Hyunchul; Song, Renming 5 2022 Homogenization of nonlocal partial differential equations related to stochastic differential equations with Lévy noise. Zbl 1504.60100 Huang, Qiao; Duan, Jinqiao; Song, Renming 4 2022 Spine decomposition and \(L \log L\) criterion for superprocesses with non-local branching mechanism. Zbl 1503.60117 Ren, Yan-Xia; Song, Renming; Yang, Ting 1 2022 Heat kernel estimates for subordinate Markov processes and their applications. Zbl 1491.60135 Cho, Soobin; Kim, Panki; Song, Renming; Vondraček, Zoran 1 2022 Stable central limit theorems for super Ornstein-Uhlenbeck processes. II. Zbl 1485.60076 Ren, Yan Xia; Song, Ren Ming; Sun, Zhen Yao; Zhao, Jian Jie 1 2022 The extremal process of super-Brownian motion. Zbl 1469.60260 Ren, Yan-Xia; Song, Renming; Zhang, Rui 9 2021 Quasi-stationary distributions for subcritical superprocesses. Zbl 1475.60155 Liu, Rongli; Ren, Yan-Xia; Song, Renming; Sun, Zhenyao 4 2021 Time fractional stochastic differential equations driven by pure jump Lévy noise. Zbl 1468.60083 Wu, Peixue; Yang, Zhiwei; Wang, Hong; Song, Renming 1 2021 Factorization and estimates of Dirichlet heat kernels for non-local operators with critical killings. Zbl 1460.60087 Cho, Soobin; Kim, Panki; Song, Renming; Vondraček, Zoran 22 2020 Sharp space-time regularity of the solution to stochastic heat equation driven by fractional-colored noise. Zbl 1447.60064 Herrell, Randall; Song, Renming; Wu, Dongsheng; Xiao, Yimin 10 2020 On the boundary theory of subordinate killed Lévy processes. Zbl 1451.60090 Kim, Panki; Song, Renming; Vondraček, Zoran 9 2020 Spine decompositions and limit theorems for a class of critical superprocesses. Zbl 1434.60250 Ren, Yan-Xia; Song, Renming; Sun, Zhenyao 7 2020 Limit theorems for a class of critical superprocesses with stable branching. Zbl 1434.60235 Ren, Yan-Xia; Song, Renming; Sun, Zhenyao 6 2020 Well-posedness and long time behavior of singular Langevin stochastic differential equations. Zbl 1457.60102 Song, Renming; Xie, Longjie 5 2020 Gradient estimates for the fundamental solution of Lévy type operator. Zbl 1434.60207 Liu, Wei; Song, Renming; Xie, Longjie 4 2020 Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradients. Zbl 1468.60096 Song, Renming; Xie, Longjie; Xie, Yingchao 2 2020 Potential theory of subordinate killed Brownian motion. Zbl 1450.60040 Kim, Panki; Song, Renming; Vondraček, Zoran 13 2019 Spectral heat content for Lévy processes. Zbl 1472.35209 Grzywny, Tomasz; Park, Hyunchul; Song, Renming 10 2019 Small time asymptotics of spectral heat contents for subordinate killed Brownian motions related to isotropic \({\alpha}\)-stable processes. Zbl 1481.60165 Park, Hyunchul; Song, Renming 8 2019 Stable central limit theorems for super Ornstein-Uhlenbeck processes. Zbl 1428.60120 Ren, Yan-Xia; Song, Renming; Sun, Zhenyao; Zhao, Jianjie 6 2019 \(L \log L\) criterion for a class of multitype superdiffusions with non-local branching mechanisms. Zbl 1420.60105 Chen, Zhen-Qing; Ren, Yan-Xia; Song, Renming 4 2019 Heat kernel estimates for Dirichlet fractional Laplacian with gradient perturbation. Zbl 1408.60069 Chen, Peng; Song, Renming; Xie, Longjie; Xie, Yingchao 4 2019 On properties of a class of strong limits for supercritical superprocesses. Zbl 1499.60281 Ren, Yanxia; Song, Renming; Zhang, Rui 1 2019 Supercritical superprocesses: proper normalization and non-degenerate strong limit. Zbl 1420.60102 Ren, Yan-Xia; Song, Renming; Zhang, Rui 1 2019 Heat kernels of non-symmetric jump processes: beyond the stable case. Zbl 1409.60116 Kim, Panki; Song, Renming; Vondraček, Zoran 25 2018 Stochastic flows for Lévy processes with Hölder drifts. Zbl 1420.60064 Chen, Zhen-Qing; Song, Renming; Zhang, Xicheng 25 2018 A 2-spine decomposition of the critical Galton-Watson tree and a probabilistic proof of Yaglom’s theorem. Zbl 1394.60089 Ren, Yan-Xia; Song, Renming; Sun, Zhenyao 10 2018 Accessibility, martin boundary and minimal thinness for Feller processes in metric measure spaces. Zbl 1395.60094 Kim, Panki; Song, Renming; Vondraček, Zoran 7 2018 Numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric Lévy motion. Zbl 1427.60085 Wang, Xiao; Duan, Jinqiao; Li, Xiaofan; Song, Renming 4 2018 Williams decomposition for superprocesses. Zbl 1387.60118 Ren, Yan-Xia; Song, Renming; Zhang, Rui 2 2018 Uniform Hausdorff dimension result for the inverse images of stable Lévy processes. Zbl 1398.60089 Song, Renming; Xiao, Yimin; Yang, Xiaochuan 1 2018 Central limit theorems for supercritical branching nonsymmetric Markov processes. Zbl 1365.60020 Ren, Yan-Xia; Song, Renming; Zhang, Rui 16 2017 Scale invariant boundary Harnack principle at infinity for Feller processes. Zbl 1381.60110 Kim, Panki; Song, Renming; Vondraček, Zoran 9 2017 Functional central limit theorems for supercritical superprocesses. Zbl 1370.60059 Ren, Yan-Xia; Song, Renming; Zhang, Rui 3 2017 Dirichlet heat kernel estimates for subordinate Brownian motions with Gaussian components. Zbl 1333.60179 Chen, Zhen-Qing; Kim, Panki; Song, Renming 17 2016 Weak extinction versus global exponential growth of total mass for superdiffusions. Zbl 1341.60102 Engländer, János; Ren, Yan-Xia; Song, Renming 6 2016 Minimal thinness with respect to subordinate killed Brownian motions. Zbl 1336.60160 Kim, Panki; Song, Renming; Vondraček, Zoran 5 2016 Minimal thinness with respect to symmetric Lévy processes. Zbl 1356.60074 Kim, Panki; Song, Renming; Vondraček, Zoran 4 2016 Martin boundary of unbounded sets for purely discontinuous Feller processes. Zbl 1351.60106 Kim, Panki; Song, Renming; Vondraček, Zoran 3 2016 Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation. Zbl 1321.60149 Chen, Zhen-Qing; Kim, Panki; Song, Renming 20 2015 Central limit theorems for supercritical superprocesses. Zbl 1325.60019 Ren, Yan-Xia; Song, Renming; Zhang, Rui 9 2015 Limit theorems for some critical superprocesses. Zbl 1338.60074 Ren, Yan-Xia; Song, Renming; Zhang, Rui 9 2015 Martin boundary for some symmetric Lévy processes. Zbl 1336.31031 Kim, Panki; Song, Renming; Vondraček, Zoran 9 2015 Strong law of large numbers for supercritical superprocesses under second moment condition. Zbl 1332.60044 Chen, Zhen-Qing; Ren, Yan-Xia; Song, Renming; Zhang, Rui 8 2015 Mean exit time and escape probability for dynamical systems driven by Lévy noises. Zbl 1318.60065 Gao, T.; Duan, J.; Li, X.; Song, R. 59 2014 Global uniform boundary Harnack principle with explicit decay rate and its application. Zbl 1296.60198 Kim, Panki; Song, Renming; Vondraček, Zoran 47 2014 Dirichlet heat kernel estimates for rotationally symmetric Lévy processes. Zbl 1304.60080 Chen, Zhen-Qing; Kim, Panki; Song, Renming 36 2014 Stable process with singular drift. Zbl 1336.60112 Kim, Panki; Song, Renming 22 2014 Quasi-stationarity and quasi-ergodicity of general Markov processes. Zbl 1309.60078 Zhang, Junfei; Li, Shoumei; Song, Renming 20 2014 Asymmetric non-Gaussian effects in a tumor growth model with immunization. Zbl 1428.92049 Hao, Mengli; Duan, Jinqiao; Song, Renming; Xu, Wei 13 2014 Central limit theorems for supercritical branching Markov processes. Zbl 1292.60034 Ren, Yan-Xia; Song, Renming; Zhang, Rui 12 2014 Central limit theorems for super Ornstein-Uhlenbeck processes. Zbl 1301.60027 Ren, Yan-Xia; Song, Renming; Zhang, Rui 8 2014 Trace estimates for relativistic stable processes. Zbl 1308.60059 Park, Hyunchul; Song, Renming 7 2014 Dirichlet heat kernel estimates for stable processes with singular drift in unbounded \(C^{1,1}\) open sets. Zbl 1301.60088 Kim, Panki; Song, Renming 7 2014 Boundary Harnack principle and Martin boundary at infinity for subordinate Brownian motions. Zbl 1302.60110 Kim, Panki; Song, Renming; Vondraček, Zoran 7 2014 Potential theory of subordinate Brownian motions with Gaussian components. Zbl 1266.31007 Kim, Panki; Song, Renming; Vondraček, Zoran 19 2013 Strong law of large numbers for a class of superdiffusions. Zbl 1260.60170 Liu, Rong-Li; Ren, Yan-Xia; Song, Renming 18 2013 Sharp estimates on the Green functions of perturbations of subordinate Brownian motions in bounded \(\kappa\)-fat open sets. Zbl 1266.60137 Kim, Panki; Park, Hyunchul; Song, Renming 4 2013 Erratum to “Lévy risk model with two-sided jumps and a barrier dividend strategy”. Zbl 1291.91094 Bo, Lijun; Song, Renming; Tang, Dan; Wang, Yongjin; Yang, Xuewei 1 2013 Bernstein functions. Theory and applications. 2nd revised and extended ed. Zbl 1257.33001 Schilling, René L.; Song, Renming; Vondraček, Zoran 377 2012 Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation. Zbl 1264.60060 Chen, Zhen-Qing; Kim, Panki; Song, Renming 57 2012 Boundary Harnack principle for \(\Delta +\Delta ^{\alpha /2}\). Zbl 1271.31006 Chen, Zhen-Qing; Kim, Panki; Song, Renming; Vondraček, Zoran 47 2012 Sharp heat kernel estimates for relativistic stable processes in open sets. Zbl 1235.60101 Chen, Zhen-Qing; Kim, Panki; Song, Renming 42 2012 Potential theory of subordinate Brownian motions revisited. Zbl 1282.60076 Kim, Panki; Song, Renming; Vondraček, Zoran 39 2012 Two-sided Green function estimates for killed subordinate Brownian motions. Zbl 1248.60091 Kim, Panki; Song, Renming; Vondraček, Zoran 33 2012 Uniform boundary Harnack principle for rotationally symmetric Lévy processes in general open sets. Zbl 1262.60077 Kim, Panki; Song, RenMing; Vondraček, Zoran 23 2012 Global heat kernel estimate for relativistic stable processes in exterior open sets. Zbl 1255.60076 Chen, Zhen-Qing; Kim, Panki; Song, Renming 19 2012 Global heat kernel estimates for relativistic stable processes in half-space-like open sets. Zbl 1239.60076 Chen, Zhen-Qing; Kim, Panki; Song, Renming 12 2012 Lévy risk model with two-sided jumps and a barrier dividend strategy. Zbl 1244.91044 Bo, Lijun; Song, Renming; Tang, Dan; Wang, Yongjin; Yang, Xuewei 11 2012 Global heat kernel estimates for \(\Delta+\Delta^{\alpha/2}\) in half-space-like domains. Zbl 1247.60115 Chen, Zhen-Qing; Kim, Panki; Song, Renming 6 2012 Minimal thinness for subordinate Brownian motion in half-space. Zbl 1273.60096 Kim, Panki; Song, Renming; Vondraček, Zoran 4 2012 Heat kernel estimates for \(\Delta +\Delta ^{\alpha /2}\) in \(C^{1, 1}\) open sets. Zbl 1229.60089 Chen, Zhen-Qing; Kim, Panki; Song, Renming 27 2011 Green function estimates for relativistic stable processes in half-space-like open sets. Zbl 1235.60100 Chen, Zhen-Qing; Kim, Panki; Song, Renming 8 2011 \(L \log L\) condition for supercritical branching Hunt processes. Zbl 1215.60050 Liu, Rong-Li; Ren, Yan-Xia; Song, Renming 7 2011 On harmonic functions for trace processes. Zbl 1227.60098 Kim, Panki; Song, Renming; Vondraček, Zoran 5 2011 On the monitoring error of the supremum of a normal jump diffusion process. Zbl 1250.60036 Chen, Ao; Feng, Liming; Song, Renming 3 2011 Selected works of Donald L. Burkholder. Edited by Burgess Davis and Renming Song. Zbl 1271.01046 Burkholder, Donald L. 2 2011 Bernstein functions. Theory and applications. Zbl 1197.33002 Schilling, René L.; Song, Renming; Vondraček, Zoran 236 2010 Heat kernel estimates for the Dirichlet fractional Laplacian. Zbl 1203.60114 Chen, Zhen-Qing; Kim, Panki; Song, Renming 122 2010 Two-sided heat kernel estimates for censored stable-like processes. Zbl 1190.60068 Chen, Zhen-Qing; Kim, Panki; Song, Renming 50 2010 Dirichlet heat kernel estimates for \(\Delta ^{\alpha /2} + \delta ^{\beta /2}\). Zbl 1268.60101 Chen, Zhen-Qing; Kim, Panki; Song, Renming 33 2010 Convexity and smoothness of scale functions and de Finetti’s control problem. Zbl 1188.93115 Kyprianou, Andreas E.; Rivero, Víctor; Song, Renming 28 2010 Sharp Green function estimates for \(\Delta + \delta ^{\alpha /2}\) in \(C^{1,1}\) open sets and their applications. Zbl 1257.31002 Chen, Zhen-Qing; Kim, Panki; Song, Renming; Vondraček, Zoran 17 2010 On the potential theory of one-dimensional subordinate Brownian motions with continuous components. Zbl 1202.60125 Kim, Panki; Song, Renming; Vondraček, Zoran 7 2010 Some remarks on special subordinators. Zbl 1196.60086 Song, Renming; Vondraček, Zoran 3 2010 Boundary Harnack principle for subordinate Brownian motions. Zbl 1166.60046 Kim, Panki; Song, Renming; Vondraček, Zoran 29 2009 Potential theory of subordinate Brownian motion. Zbl 1203.60118 Song, R.; Vondraček, Z. 23 2009 \(L \log L\) criterion for a class of superdiffusions. Zbl 1175.60077 Liu, Rong-Li; Ren, Yan-Xia; Song, Renming 20 2009 Intrinsic ultracontractivity for non-symmetric Lévy processes. Zbl 1175.47040 Kim, Panki; Song, Renming 15 2009 A class of stochastic partial differential equations for interacting superprocesses on a bounded domain. Zbl 1170.60034 Ren, Yan-Xia; Song, Renming; Wang, Hao 2 2009 Erratum to: “Intrinsic ultracontractivity for non-symmetric Lévy processes” [Forum Math. 21 (2009) 43-66]. Zbl 1179.47040 Kim, Panki; Song, Renming 1 2009 Intrinsic ultracontractivity of non-symmetric diffusion semigroups in bounded domains. Zbl 1167.60017 Kim, Panki; Song, Renming 25 2008 On the relationship between subordinate killed and killed subordinate processes. Zbl 1187.60057 Song, Renming; Vondracek, Zoran 22 2008 ...and 46 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,609 Authors 103 Song, Renming 78 Kim, Panki 74 Chen, Zhen-Qing 53 Qi, Feng 38 Vondraček, Zoran 36 Ren, Yanxia 36 Wang, Jian 31 Duan, Jinqiao 28 Bogdan, Krzysztof 27 Guo, Bai-Ni 24 Schilling, René Leander 23 Kyprianou, Andreas E. 21 Kwaśnicki, Mateusz 20 Grzywny, Tomasz 19 Jakubowski, Tomasz 17 Kulczycki, Tadeusz 16 Kaleta, Kamil 16 Kumagai, Takashi 16 Ryznar, Michał 16 Vazquez, Juan Luis 15 Patie, Pierre 14 Zhang, Xicheng 13 Chen, Huyuan 13 Lörinczi, József 13 Mimica, Ante 13 Nane, Erkan 12 Deng, Changsong 11 Biswas, Anup 11 Dipierro, Serena 11 Kurths, Jürgen 11 Kuwae, Kazuhiro 11 Mai, Jan-Frederik 11 Porcu, Emilio 11 Ros-Oton, Xavier 11 Valdinoci, Enrico 11 Xie, Longjie 11 Zhang, Rui 10 Ascione, Giacomo 10 Kühn, Franziska 10 Park, Hyunchul 10 Xu, Wei 10 Zhang, Tusheng S. 9 Bañuelos, Rodrigo 9 Beghin, Luisa 9 Deng, Weihua 9 Kim, Daehong 9 Li, Lingfei 9 Li, Xiaofan 9 Metzler, Ralf 8 Bass, Richard F. 8 Bonforte, Matteo 8 Chechkin, Aleksei V. 8 Chen, Xin 8 D’Ovidio, Mirko 8 Gomilko, Alexandre M. 8 Górska, Katarzyna 8 Grubb, Gerd 8 Kim, KyeongHun 8 Mâagli, Habib 8 Mendoza-Arriaga, Rafael 8 Menegatto, Valdir Antonio 8 Sandev, Trifce 8 Sandrić, Nikola 8 Szczypkowski, Karol 8 Sztonyk, Paweł 8 Toaldo, Bruno 8 Tomilov, Yuri 8 Tsuchida, Kaneharu 8 Yang, Ting 8 Zhang, Hongxia 7 Acuña Valverde, Luis 7 Bazhlekova, Emilia G. 7 Foondun, Mohammud 7 Garain, Prashanta 7 Horzela, Andrzej 7 Jacob, Niels 7 Jarohs, Sven 7 Karp, Dmitriĭ Borisovich 7 Leżaj, Łukasz 7 Linetsky, Vadim 7 Liu, Rongli 7 Małecki, Jacek 7 Meerschaert, Mark Marvin 7 Pardo, Juan Carlos 7 Pedersen, Henrik Laurberg 7 Pietruska-Pałuba, Katarzyna 7 Scherer, Matthias 7 Simon, Thomas 7 Sire, Yannick 7 Wang, Feng-Yu 7 Yang, Xuewei 7 Yin, Chuancun 6 Caffarelli, Luis Ángel 6 Cho, Soobin 6 Dyda, Bartłomiej 6 Jedidi, Wissem 6 Kang, Jaehoon 6 Kim, Ildoo 6 Lee, Ki-Ahm 6 Leonenko, Nikolai N. ...and 1,509 more Authors all top 5 Cited in 326 Serials 82 Stochastic Processes and their Applications 79 Potential Analysis 59 Journal of Mathematical Analysis and Applications 57 Journal of Functional Analysis 47 Fractional Calculus & Applied Analysis 46 Journal of Theoretical Probability 40 Transactions of the American Mathematical Society 39 Journal of Differential Equations 28 The Annals of Probability 27 Statistics & Probability Letters 26 Probability Theory and Related Fields 25 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 23 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 21 Mathematische Nachrichten 21 Electronic Journal of Probability 19 Proceedings of the American Mathematical Society 18 Bernoulli 17 Mathematische Annalen 16 Journal of Evolution Equations 16 ALEA. Latin American Journal of Probability and Mathematical Statistics 15 Chaos, Solitons and Fractals 15 Science China. Mathematics 14 Journal of Computational and Applied Mathematics 14 Discrete and Continuous Dynamical Systems 13 Journal of Physics A: Mathematical and Theoretical 12 Communications in Mathematical Physics 12 Journal of Statistical Physics 12 Journal of the London Mathematical Society. Second Series 12 Mathematische Zeitschrift 12 The Annals of Applied Probability 12 Communications in Nonlinear Science and Numerical Simulation 12 Stochastics and Dynamics 11 Advances in Applied Probability 11 Applied Mathematics and Computation 11 Journal of Applied Probability 11 Stochastic Analysis and Applications 11 The Journal of Geometric Analysis 10 Journal de Mathématiques Pures et Appliquées. Neuvième Série 10 Mathematical Inequalities & Applications 10 Chaos 9 Journal of Mathematical Physics 9 Forum Mathematicum 8 Computers & Mathematics with Applications 8 Physica A 8 ZAMP. Zeitschrift für angewandte Mathematik und Physik 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Journal of the European Mathematical Society (JEMS) 8 Discrete and Continuous Dynamical Systems. Series B 7 Journal of Computational Physics 7 Nonlinearity 7 Studia Mathematica 7 Fuzzy Sets and Systems 7 Insurance Mathematics & Economics 7 Probability and Mathematical Statistics 7 Acta Applicandae Mathematicae 7 SIAM Journal on Mathematical Analysis 7 Calculus of Variations and Partial Differential Equations 7 Positivity 7 Acta Mathematica Sinica. English Series 6 Mathematical Methods in the Applied Sciences 6 Advances in Mathematics 6 Illinois Journal of Mathematics 6 Results in Mathematics 6 Tôhoku Mathematical Journal. Second Series 6 Communications in Partial Differential Equations 6 Finance and Stochastics 6 Communications on Pure and Applied Analysis 6 Mediterranean Journal of Mathematics 6 Stochastics 6 Applicable Analysis and Discrete Mathematics 6 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 5 Mathematical Notes 5 Integral Equations and Operator Theory 5 Journal of the Mathematical Society of Japan 5 Applied Mathematics Letters 5 Linear Algebra and its Applications 5 Theory of Probability and Mathematical Statistics 5 Mathematical Finance 5 Frontiers of Mathematics in China 5 Dependence Modeling 5 Modern Stochastics. Theory and Applications 4 Communications on Pure and Applied Mathematics 4 Journal d’Analyse Mathématique 4 Reviews in Mathematical Physics 4 Applied Mathematics and Optimization 4 BIT 4 Journal of Approximation Theory 4 Proceedings of the London Mathematical Society. Third Series 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Constructive Approximation 4 Revista Matemática Iberoamericana 4 Filomat 4 NoDEA. Nonlinear Differential Equations and Applications 4 Electronic Communications in Probability 4 Communications in Contemporary Mathematics 4 Stochastic Models 4 Advanced Nonlinear Studies 4 Analysis & PDE 4 Stochastic and Partial Differential Equations. Analysis and Computations 4 Problemy Analiza. Issues of Analysis ...and 226 more Serials all top 5 Cited in 49 Fields 995 Probability theory and stochastic processes (60-XX) 600 Partial differential equations (35-XX) 269 Operator theory (47-XX) 214 Real functions (26-XX) 143 Potential theory (31-XX) 117 Special functions (33-XX) 77 Numerical analysis (65-XX) 70 Statistical mechanics, structure of matter (82-XX) 68 Harmonic analysis on Euclidean spaces (42-XX) 66 Statistics (62-XX) 66 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 65 Integral transforms, operational calculus (44-XX) 60 Integral equations (45-XX) 60 Functional analysis (46-XX) 42 Ordinary differential equations (34-XX) 42 Dynamical systems and ergodic theory (37-XX) 39 Biology and other natural sciences (92-XX) 38 Functions of a complex variable (30-XX) 31 Number theory (11-XX) 31 Systems theory; control (93-XX) 28 Combinatorics (05-XX) 22 Measure and integration (28-XX) 22 Calculus of variations and optimal control; optimization (49-XX) 22 Global analysis, analysis on manifolds (58-XX) 21 Quantum theory (81-XX) 19 Fluid mechanics (76-XX) 16 Linear and multilinear algebra; matrix theory (15-XX) 15 Approximations and expansions (41-XX) 15 Abstract harmonic analysis (43-XX) 12 Difference and functional equations (39-XX) 9 Mechanics of deformable solids (74-XX) 8 Operations research, mathematical programming (90-XX) 7 Geophysics (86-XX) 6 Sequences, series, summability (40-XX) 5 Optics, electromagnetic theory (78-XX) 4 Group theory and generalizations (20-XX) 4 Differential geometry (53-XX) 4 Computer science (68-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Convex and discrete geometry (52-XX) 3 Information and communication theory, circuits (94-XX) 2 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Manifolds and cell complexes (57-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.