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 Homepage: http://www.math.uiuc.edu/~rsong/ External Links: MGP · ORCID · ResearchGate · dblp · GND Documents Indexed: 157 Publications since 1984, including 2 Books 2 Contributions as Editor Reviewing Activity: 108 Reviews Co-Authors: 58 Co-Authors with 149 Joint Publications 1,851 Co-Co-Authors all top 5 Co-Authors 10 single-authored 52 Kim, Panki 42 Vondraček, Zoran 30 Chen, Zhen-Qing 29 Ren, Yanxia 11 Zhang, Rui 8 Rao, Murali 7 Glover, Joseph 7 Sun, Zhenyao 6 Liu, Rongli 5 Park, Hyunchul 5 Šikić, Hrvoje 5 Xie, Longjie 4 Duan, Jinqiao 3 Ma, Zhi-Ming 2 Bo, Lijun 2 Cho, Soobin 2 Conlon, Joseph G. 2 Li, Xiaofan 2 Schilling, René Leander 2 Tang, Dan 2 Wang, Yongjin 2 Xiao, Yimin 2 Xie, Yingchao 2 Yang, Xuewei 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 Hou, Haojie 1 Huang, Qiao 1 Kyprianou, Andreas E. 1 Li, Shoumei 1 Li, Zhichan 1 Liu, Wei 1 Olsen, Peder A. 1 Pop-Stojanovic, Zoran R. 1 Rivero, Víctor Manuel 1 Sowers, Richard B. 1 Wang, Hao 1 Wang, Hong 1 Wang, Xiao 1 Wu, Dongsheng 1 Wu, Jang-Mei 1 Wu, Peixue 1 Xu, Wei 1 Yang, Ting 1 Yang, Xiaochuan 1 Yang, Zhiwei 1 Zhang, Junfei 1 Zhang, Xicheng 1 Zhou, Xianyin all top 5 Serials 16 Stochastic Processes and their Applications 11 Potential Analysis 9 Journal of Functional Analysis 9 Probability Theory and Related Fields 7 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 Electronic Communications in Probability 3 Journal of Differential Equations 3 Mathematische Zeitschrift 3 Tôhoku Mathematical Journal. Second Series 3 Acta Mathematicae Applicatae Sinica. English Series 3 Forum Mathematicum 2 Journal of Mathematical Analysis and Applications 2 Journal of Statistical Physics 2 Journal of Applied Probability 2 Mathematische Annalen 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 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 De Gruyter Studies in Mathematics 1 Advances in Applied Probability 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 Journal of the European Mathematical Society (JEMS) 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 149 Probability theory and stochastic processes (60-XX) 30 Potential theory (31-XX) 27 Operator theory (47-XX) 19 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 Numerical analysis (65-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 Statistics (62-XX) 1 Quantum theory (81-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 140 Publications have been cited 2,551 times in 1,315 Documents Cited by ▼ Year ▼ Bernstein functions. Theory and applications. 2nd revised and extended ed. Zbl 1257.33001Schilling, René L.; Song, Renming; Vondraček, Zoran 231 2012 Bernstein functions. Theory and applications. Zbl 1197.33002Schilling, René L.; Song, Renming; Vondraček, Zoran 134 2010 Estimates on Green functions and Poisson kernels for symmetric stable processes. Zbl 0918.60068Chen, Zhen-Qing; Song, Renming 114 1998 Heat kernel estimates for the Dirichlet fractional Laplacian. Zbl 1203.60114Chen, Zhen-Qing; Kim, Panki; Song, Renming 112 2010 Two-sided eigenvalue estimates for subordinate processes in domains. Zbl 1081.60056Chen, Zhen-Qing; Song, Renming 75 2005 Intrinsic ultracontractivity and conditional gauge for symmetric stable processes. Zbl 0886.60072Chen, Zhen-Qing; Song, Renming 62 1997 Drift transforms and Green function estimates for discontinuous processes. Zbl 1031.60071Chen, Zhen-Qing; Song, Renming 58 2003 Potential theory of subordinate killed Brownian motion in a domain. Zbl 1022.60078Song, Renming; Vondraček, Zoran 55 2003 Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation. Zbl 1264.60060Chen, Zhen-Qing; Kim, Panki; Song, Renming 55 2012 Mean exit time and escape probability for dynamical systems driven by Lévy noises. Zbl 1318.60065Gao, T.; Duan, J.; Li, X.; Song, R. 51 2014 Boundary Harnack principle for symmetric stable processes. Zbl 0945.31006Song, Renming; Wu, Jang-Mei 50 1999 Harnack inequality for some classes of Markov processes. Zbl 1052.60064Song, Renming; Vondraček, Zoran 48 2004 Two-sided heat kernel estimates for censored stable-like processes. Zbl 1190.60068Chen, Zhen-Qing; Kim, Panki; Song, Renming 44 2010 General gauge and conditional gauge theorems. Zbl 1017.60086Chen, Zhen-Qing; Song, Renming 39 2002 Global uniform boundary Harnack principle with explicit decay rate and its application. Zbl 1296.60198Kim, Panki; Song, Renming; Vondraček, Zoran 39 2014 Conditional gauge theorem for non-local Feynman-Kac transforms. Zbl 1025.60032Chen, Zhen-Qing; Song, Renming 38 2003 Sharp heat kernel estimates for relativistic stable processes in open sets. Zbl 1235.60101Chen, Zhen-Qing; Kim, Panki; Song, Renming 38 2012 Green function estimates and Harnack inequality for subordinate Brownian motions. Zbl 1107.60042Rao, Murali; Song, Renming; Vondraček, Zoran 37 2006 Boundary Harnack principle for \(\Delta +\Delta ^{\alpha /2}\). Zbl 1271.31006Chen, Zhen-Qing; Kim, Panki; Song, Renming; Vondraček, Zoran 37 2012 Potential theory of subordinate Brownian motions revisited. Zbl 1282.60076Kim, Panki; Song, Renming; Vondraček, Zoran 36 2012 Martin boundary and integral representation for harmonic functions of symmetric stable processes. Zbl 0954.60003Chen, Zhen-Qing; Song, Renming 33 1998 Two-sided estimates on the density of Brownian motion with singular drift. Zbl 1110.60071Kim, Panki; Song, Renming 32 2006 Hardy inequality for censored stable processes. Zbl 1070.46021Chen, Zhen-Qing; Song, Renming 29 2003 Two-sided Green function estimates for killed subordinate Brownian motions. Zbl 1248.60091Kim, Panki; Song, Renming; Vondraček, Zoran 29 2012 Dirichlet heat kernel estimates for rotationally symmetric Lévy processes. Zbl 1304.60080Chen, Zhen-Qing; Kim, Panki; Song, Renming 29 2014 Boundary Harnack principle for subordinate Brownian motions. Zbl 1166.60046Kim, Panki; Song, Renming; Vondraček, Zoran 27 2009 Convexity and smoothness of scale functions and de Finetti’s control problem. Zbl 1188.93115Kyprianou, Andreas E.; Rivero, Víctor; Song, Renming 26 2010 Dirichlet heat kernel estimates for \(\Delta ^{\alpha /2} + \delta ^{\beta /2}\). Zbl 1268.60101Chen, Zhen-Qing; Kim, Panki; Song, Renming 26 2010 Intrinsic ultracontractivity, conditional lifetimes and conditional gauge for symmetric stable processes on rough domains. Zbl 0959.60035Chen, Zhen-Qing; Song, Renming 24 2000 Potential theory of truncated stable processes. Zbl 1115.60073Kim, Panki; Song, Renming 24 2007 Heat kernel estimates for \(\Delta +\Delta ^{\alpha /2}\) in \(C^{1, 1}\) open sets. Zbl 1229.60089Chen, Zhen-Qing; Kim, Panki; Song, Renming 24 2011 Intrinsic ultracontractivity of non-symmetric diffusion semigroups in bounded domains. Zbl 1167.60017Kim, Panki; Song, Renming 23 2008 Potential theory of special subordinators and subordinate killed stable processes. Zbl 1119.60063Song, Renming; Vondraček, Zoran 22 2006 Uniform boundary Harnack principle for rotationally symmetric Lévy processes in general open sets. Zbl 1262.60077Kim, Panki; Song, RenMing; Vondraček, Zoran 22 2012 Potential theory of subordinate Brownian motion. Zbl 1203.60118Song, R.; Vondraček, Z. 22 2009 Potential theory of geometric stable processes. Zbl 1099.60051Šikić, Hrvoje; Song, Renming; Vondraček, Zoran 21 2006 On the relationship between subordinate killed and killed subordinate processes. Zbl 1187.60057Song, Renming; Vondracek, Zoran 21 2008 Stable process with singular drift. Zbl 1336.60112Kim, Panki; Song, Renming 21 2014 Stochastic flows for Lévy processes with Hölder drifts. Zbl 1420.60064Chen, Zhen-Qing; Song, Renming; Zhang, Xicheng 21 2018 Heat kernels of non-symmetric jump processes: beyond the stable case. Zbl 1409.60116Kim, Panki; Song, Renming; Vondraček, Zoran 21 2018 A remark on diffusion of directed polymers in random environments. Zbl 0924.60053Song, Renming; Zhou, Xian Yin 19 1996 \(L \log L\) criterion for a class of superdiffusions. Zbl 1175.60077Liu, Rong-Li; Ren, Yan-Xia; Song, Renming 19 2009 Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation. Zbl 1321.60149Chen, Zhen-Qing; Kim, Panki; Song, Renming 19 2015 Strong law of large numbers for a class of superdiffusions. Zbl 1260.60170Liu, Rong-Li; Ren, Yan-Xia; Song, Renming 18 2013 Potential theory of subordinate Brownian motions with Gaussian components. Zbl 1266.31007Kim, Panki; Song, Renming; Vondraček, Zoran 18 2013 Estimates on the Dirichlet heat kernel of domains above the graphs of bounded \(C^{1,1}\) functions. Zbl 1064.35066Song, Renming 17 2004 Global heat kernel estimate for relativistic stable processes in exterior open sets. Zbl 1255.60076Chen, Zhen-Qing; Kim, Panki; Song, Renming 17 2012 Dirichlet heat kernel estimates for subordinate Brownian motions with Gaussian components. Zbl 1333.60179Chen, Zhen-Qing; Kim, Panki; Song, Renming 16 2016 Parabolic Harnack inequality for the mixture of Brownian motion and stable process. Zbl 1143.60049Song, Renming; Vondraček, Zoran 15 2007 Intrinsic ultracontractivity for non-symmetric Lévy processes. Zbl 1175.47040Kim, Panki; Song, Renming 15 2009 Sharp bounds on the density, Green function and jumping function of subordinate killed BM. Zbl 1054.60080Song, Renming 14 2004 Central limit theorems for supercritical branching nonsymmetric Markov processes. Zbl 1365.60020Ren, Yan-Xia; Song, Renming; Zhang, Rui 14 2017 Estimates on Green functions and Schrödinger-type equations for non-symmetric diffusions with measure-valued drifts. Zbl 1118.35007Kim, Panki; Song, Renming 13 2007 Intrinsic ultracontractivity of nonsymmetric diffusions with measure-valued drifts and potentials. Zbl 1175.47039Kim, Panki; Song, Renming 13 2008 Continuity of eigenvalues of subordinate processes in domains. Zbl 1090.60070Chen, Zhen-Qing; Song, Renming 12 2006 Boundary behavior of harmonic functions for truncated stable processes. Zbl 1145.60026Kim, Panki; Song, Renming 12 2008 Sharp Green function estimates for \(\Delta + \delta ^{\alpha /2}\) in \(C^{1,1}\) open sets and their applications. Zbl 1257.31002Chen, Zhen-Qing; Kim, Panki; Song, Renming; Vondraček, Zoran 12 2010 Global heat kernel estimates for relativistic stable processes in half-space-like open sets. Zbl 1239.60076Chen, Zhen-Qing; Kim, Panki; Song, Renming 12 2012 Harnack inequality for some discontinuous Markov processes with a diffusion part. Zbl 1075.60096Song, Renming; Vondraček, Zoran 12 2005 Quasi-stationarity and quasi-ergodicity of general Markov processes. Zbl 1309.60078Zhang, Junfei; Li, Shoumei; Song, Renming 12 2014 Asymmetric non-Gaussian effects in a tumor growth model with immunization. Zbl 1428.92049Hao, Mengli; Duan, Jinqiao; Song, Renming; Xu, Wei 12 2014 Factorization and estimates of Dirichlet heat kernels for non-local operators with critical killings. Zbl 1460.60087Cho, Soobin; Kim, Panki; Song, Renming; Vondraček, Zoran 12 2020 On suprema of Lévy processes and application in risk theory. Zbl 1178.60036Song, Renming; Vondraček, Zoran 11 2008 Two-sided estimates on the density of the Feynman-Kac semigroups of stable-like processes. Zbl 1112.60059Song, Renming 11 2006 Lévy risk model with two-sided jumps and a barrier dividend strategy. Zbl 1244.91044Bo, Lijun; Song, Renming; Tang, Dan; Wang, Yongjin; Yang, Xuewei 11 2012 Quadratic forms corresponding to the generalized Schrödinger semigroups. Zbl 0807.60056Glover, J.; Rao, M.; Šikić, H.; Song, R. 11 1994 Central limit theorems for supercritical branching Markov processes. Zbl 1292.60034Ren, Yan-Xia; Song, Renming; Zhang, Rui 11 2014 On dual processes of non-symmetric diffusions with measure-valued drifts. Zbl 1146.60060Kim, Panki; Song, Renming 10 2008 Feynman-Kac semigroup with discontinuous additive functionals. Zbl 0831.60085Song, Renming 9 1995 Application of Carleson’s theorem to wavelet inversion. Zbl 0816.42018Rao, Murali; Šikić, Hrvoje; Song, Renming 9 1994 Central limit theorems for supercritical superprocesses. Zbl 1325.60019Ren, Yan-Xia; Song, Renming; Zhang, Rui 9 2015 Boundary Harnack principle for Brownian motions with measure-valued drifts in bounded Lipschitz domains. Zbl 1140.60038Kim, Panki; Song, Renming 8 2007 On the (N) fuzzy integral. Zbl 0641.28014Song, Renming 8 1985 Probabilistic approach to the Dirichlet problem of perturbed stable processes. Zbl 0792.60067Song, Renming 8 1993 Limit theorems for some critical superprocesses. Zbl 1338.60074Ren, Yan-Xia; Song, Renming; Zhang, Rui 8 2015 Martin boundary for some symmetric Lévy processes. Zbl 1336.31031Kim, Panki; Song, Renming; Vondraček, Zoran 8 2015 Strong law of large numbers for supercritical superprocesses under second moment condition. Zbl 1332.60044Chen, Zhen-Qing; Ren, Yan-Xia; Song, Renming; Zhang, Rui 8 2015 Scale invariant boundary Harnack principle at infinity for Feller processes. Zbl 1381.60110Kim, Panki; Song, Renming; Vondraček, Zoran 8 2017 Central limit theorems for super Ornstein-Uhlenbeck processes. Zbl 1301.60027Ren, Yan-Xia; Song, Renming; Zhang, Rui 8 2014 Spectral heat content for Lévy processes. Zbl 1472.35209Grzywny, Tomasz; Park, Hyunchul; Song, Renming 8 2019 Potential theory of subordinate killed Brownian motion. Zbl 1450.60040Kim, Panki; Song, Renming; Vondraček, Zoran 8 2019 Diffusion of directed polymers in a strong random environment. Zbl 1081.82626Olsen, Peder; Song, Renming 7 1996 Green function estimates for relativistic stable processes in half-space-like open sets. Zbl 1235.60100Chen, Zhen-Qing; Kim, Panki; Song, Renming 7 2011 On the potential theory of one-dimensional subordinate Brownian motions with continuous components. Zbl 1202.60125Kim, Panki; Song, Renming; Vondraček, Zoran 7 2010 Dirichlet heat kernel estimates for stable processes with singular drift in unbounded \(C^{1,1}\) open sets. Zbl 1301.60088Kim, Panki; Song, Renming 7 2014 \(L \log L\) condition for supercritical branching Hunt processes. Zbl 1215.60050Liu, Rong-Li; Ren, Yan-Xia; Song, Renming 7 2011 Trace estimates for relativistic stable processes. Zbl 1308.60059Park, Hyunchul; Song, Renming 7 2014 A 2-spine decomposition of the critical Galton-Watson tree and a probabilistic proof of Yaglom’s theorem. Zbl 1394.60089Ren, Yan-Xia; Song, Renming; Sun, Zhenyao 7 2018 Sharp space-time regularity of the solution to stochastic heat equation driven by fractional-colored noise. Zbl 1447.60064Herrell, Randall; Song, Renming; Wu, Dongsheng; Xiao, Yimin 7 2020 Harmonic functions of subordinate killed Brownian motion. Zbl 1061.60077Glover, J.; Pop-Stojanovic, Z.; Rao, M.; Šikić, H.; Song, R.; Vondraček, Z. 6 2004 Global heat kernel estimates for \(\Delta+\Delta^{\alpha/2}\) in half-space-like domains. Zbl 1247.60115Chen, Zhen-Qing; Kim, Panki; Song, Renming 6 2012 Weak extinction versus global exponential growth of total mass for superdiffusions. Zbl 1341.60102Engländer, János; Ren, Yan-Xia; Song, Renming 6 2016 Boundary Harnack principle and Martin boundary at infinity for subordinate Brownian motions. Zbl 1302.60110Kim, Panki; Song, Renming; Vondraček, Zoran 6 2014 Spine decompositions and limit theorems for a class of critical superprocesses. Zbl 1434.60250Ren, Yan-Xia; Song, Renming; Sun, Zhenyao 6 2020 Accessibility, martin boundary and minimal thinness for Feller processes in metric measure spaces. Zbl 1395.60094Kim, Panki; Song, Renming; Vondraček, Zoran 6 2018 Small time asymptotics of spectral heat contents for subordinate killed Brownian motions related to isotropic \({\alpha}\)-stable processes. Zbl 1481.60165Park, Hyunchul; Song, Renming 6 2019 Probabilistic methods in Schrödinger equations. Zbl 0691.60050Ma, Zhiming; Song, Renming 5 1990 On the boundary theory of subordinate killed Lévy processes. Zbl 1451.60090Kim, Panki; Song, Renming; Vondraček, Zoran 5 2020 Minimal thinness for subordinate Brownian motion in half-space. Zbl 1273.60096Kim, Panki; Song, Renming; Vondraček, Zoran 4 2012 \(\Gamma\)-potentials. Zbl 0873.60052Glover, Joseph; Rao, Murali; Šikić, Hrvoje; Song, Renming 4 1994 On potential theory of Markov processes with jump kernels decaying at the boundary. Zbl 1508.60079Kim, Panki; Song, Renming; Vondraček, Zoran 3 2023 Branching Brownian motion in a periodic environment and uniqueness of pulsating traveling waves. Zbl 1518.60083Ren, Yan-Xia; Song, Renming; Yang, Fan 1 2023 Positive self-similar Markov processes obtained by resurrection. Zbl 1508.60048Kim, Panki; Song, Renming; Vondraček, Zoran 1 2023 Spectral heat content for \(\alpha \)-stable processes in \({C^{1,1}}\) open sets. Zbl 1486.60066Park, Hyunchul; Song, Renming 2 2022 Spine decomposition and \(L \log L\) criterion for superprocesses with non-local branching mechanism. Zbl 1503.60117Ren, Yan-Xia; Song, Renming; Yang, Ting 1 2022 Stable central limit theorems for super Ornstein-Uhlenbeck processes. II. Zbl 1485.60076Ren, Yan Xia; Song, Ren Ming; Sun, Zhen Yao; Zhao, Jian Jie 1 2022 Homogenization of nonlocal partial differential equations related to stochastic differential equations with Lévy noise. Zbl 1504.60100Huang, Qiao; Duan, Jinqiao; Song, Renming 1 2022 The extremal process of super-Brownian motion. Zbl 1469.60260Ren, Yan-Xia; Song, Renming; Zhang, Rui 3 2021 Quasi-stationary distributions for subcritical superprocesses. Zbl 1475.60155Liu, Rongli; Ren, Yan-Xia; Song, Renming; Sun, Zhenyao 2 2021 Factorization and estimates of Dirichlet heat kernels for non-local operators with critical killings. Zbl 1460.60087Cho, Soobin; Kim, Panki; Song, Renming; Vondraček, Zoran 12 2020 Sharp space-time regularity of the solution to stochastic heat equation driven by fractional-colored noise. Zbl 1447.60064Herrell, Randall; Song, Renming; Wu, Dongsheng; Xiao, Yimin 7 2020 Spine decompositions and limit theorems for a class of critical superprocesses. Zbl 1434.60250Ren, Yan-Xia; Song, Renming; Sun, Zhenyao 6 2020 On the boundary theory of subordinate killed Lévy processes. Zbl 1451.60090Kim, Panki; Song, Renming; Vondraček, Zoran 5 2020 Limit theorems for a class of critical superprocesses with stable branching. Zbl 1434.60235Ren, Yan-Xia; Song, Renming; Sun, Zhenyao 4 2020 Gradient estimates for the fundamental solution of Lévy type operator. Zbl 1434.60207Liu, Wei; Song, Renming; Xie, Longjie 3 2020 Well-posedness and long time behavior of singular Langevin stochastic differential equations. Zbl 1457.60102Song, Renming; Xie, Longjie 3 2020 Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradients. Zbl 1468.60096Song, Renming; Xie, Longjie; Xie, Yingchao 1 2020 Spectral heat content for Lévy processes. Zbl 1472.35209Grzywny, Tomasz; Park, Hyunchul; Song, Renming 8 2019 Potential theory of subordinate killed Brownian motion. Zbl 1450.60040Kim, Panki; Song, Renming; Vondraček, Zoran 8 2019 Small time asymptotics of spectral heat contents for subordinate killed Brownian motions related to isotropic \({\alpha}\)-stable processes. Zbl 1481.60165Park, Hyunchul; Song, Renming 6 2019 Stable central limit theorems for super Ornstein-Uhlenbeck processes. Zbl 1428.60120Ren, Yan-Xia; Song, Renming; Sun, Zhenyao; Zhao, Jianjie 4 2019 \(L \log L\) criterion for a class of multitype superdiffusions with non-local branching mechanisms. Zbl 1420.60105Chen, Zhen-Qing; Ren, Yan-Xia; Song, Renming 4 2019 Heat kernel estimates for Dirichlet fractional Laplacian with gradient perturbation. Zbl 1408.60069Chen, Peng; Song, Renming; Xie, Longjie; Xie, Yingchao 3 2019 On properties of a class of strong limits for supercritical superprocesses. Zbl 1499.60281Ren, Yanxia; Song, Renming; Zhang, Rui 1 2019 Supercritical superprocesses: proper normalization and non-degenerate strong limit. Zbl 1420.60102Ren, Yan-Xia; Song, Renming; Zhang, Rui 1 2019 Stochastic flows for Lévy processes with Hölder drifts. Zbl 1420.60064Chen, Zhen-Qing; Song, Renming; Zhang, Xicheng 21 2018 Heat kernels of non-symmetric jump processes: beyond the stable case. Zbl 1409.60116Kim, Panki; Song, Renming; Vondraček, Zoran 21 2018 A 2-spine decomposition of the critical Galton-Watson tree and a probabilistic proof of Yaglom’s theorem. Zbl 1394.60089Ren, Yan-Xia; Song, Renming; Sun, Zhenyao 7 2018 Accessibility, martin boundary and minimal thinness for Feller processes in metric measure spaces. Zbl 1395.60094Kim, Panki; Song, Renming; Vondraček, Zoran 6 2018 Numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric Lévy motion. Zbl 1427.60085Wang, Xiao; Duan, Jinqiao; Li, Xiaofan; Song, Renming 4 2018 Uniform Hausdorff dimension result for the inverse images of stable Lévy processes. Zbl 1398.60089Song, Renming; Xiao, Yimin; Yang, Xiaochuan 1 2018 Williams decomposition for superprocesses. Zbl 1387.60118Ren, Yan-Xia; Song, Renming; Zhang, Rui 1 2018 Central limit theorems for supercritical branching nonsymmetric Markov processes. Zbl 1365.60020Ren, Yan-Xia; Song, Renming; Zhang, Rui 14 2017 Scale invariant boundary Harnack principle at infinity for Feller processes. Zbl 1381.60110Kim, Panki; Song, Renming; Vondraček, Zoran 8 2017 Functional central limit theorems for supercritical superprocesses. Zbl 1370.60059Ren, Yan-Xia; Song, Renming; Zhang, Rui 3 2017 Dirichlet heat kernel estimates for subordinate Brownian motions with Gaussian components. Zbl 1333.60179Chen, Zhen-Qing; Kim, Panki; Song, Renming 16 2016 Weak extinction versus global exponential growth of total mass for superdiffusions. Zbl 1341.60102Engländer, János; Ren, Yan-Xia; Song, Renming 6 2016 Minimal thinness with respect to subordinate killed Brownian motions. Zbl 1336.60160Kim, Panki; Song, Renming; Vondraček, Zoran 4 2016 Minimal thinness with respect to symmetric Lévy processes. Zbl 1356.60074Kim, Panki; Song, Renming; Vondraček, Zoran 4 2016 Martin boundary of unbounded sets for purely discontinuous Feller processes. Zbl 1351.60106Kim, Panki; Song, Renming; Vondraček, Zoran 3 2016 Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation. Zbl 1321.60149Chen, Zhen-Qing; Kim, Panki; Song, Renming 19 2015 Central limit theorems for supercritical superprocesses. Zbl 1325.60019Ren, Yan-Xia; Song, Renming; Zhang, Rui 9 2015 Limit theorems for some critical superprocesses. Zbl 1338.60074Ren, Yan-Xia; Song, Renming; Zhang, Rui 8 2015 Martin boundary for some symmetric Lévy processes. Zbl 1336.31031Kim, Panki; Song, Renming; Vondraček, Zoran 8 2015 Strong law of large numbers for supercritical superprocesses under second moment condition. Zbl 1332.60044Chen, 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 1318.60065Gao, T.; Duan, J.; Li, X.; Song, R. 51 2014 Global uniform boundary Harnack principle with explicit decay rate and its application. Zbl 1296.60198Kim, Panki; Song, Renming; Vondraček, Zoran 39 2014 Dirichlet heat kernel estimates for rotationally symmetric Lévy processes. Zbl 1304.60080Chen, Zhen-Qing; Kim, Panki; Song, Renming 29 2014 Stable process with singular drift. Zbl 1336.60112Kim, Panki; Song, Renming 21 2014 Quasi-stationarity and quasi-ergodicity of general Markov processes. Zbl 1309.60078Zhang, Junfei; Li, Shoumei; Song, Renming 12 2014 Asymmetric non-Gaussian effects in a tumor growth model with immunization. Zbl 1428.92049Hao, Mengli; Duan, Jinqiao; Song, Renming; Xu, Wei 12 2014 Central limit theorems for supercritical branching Markov processes. Zbl 1292.60034Ren, Yan-Xia; Song, Renming; Zhang, Rui 11 2014 Central limit theorems for super Ornstein-Uhlenbeck processes. Zbl 1301.60027Ren, Yan-Xia; Song, Renming; Zhang, Rui 8 2014 Dirichlet heat kernel estimates for stable processes with singular drift in unbounded \(C^{1,1}\) open sets. Zbl 1301.60088Kim, Panki; Song, Renming 7 2014 Trace estimates for relativistic stable processes. Zbl 1308.60059Park, Hyunchul; Song, Renming 7 2014 Boundary Harnack principle and Martin boundary at infinity for subordinate Brownian motions. Zbl 1302.60110Kim, Panki; Song, Renming; Vondraček, Zoran 6 2014 Strong law of large numbers for a class of superdiffusions. Zbl 1260.60170Liu, Rong-Li; Ren, Yan-Xia; Song, Renming 18 2013 Potential theory of subordinate Brownian motions with Gaussian components. Zbl 1266.31007Kim, Panki; Song, Renming; Vondraček, Zoran 18 2013 Sharp estimates on the Green functions of perturbations of subordinate Brownian motions in bounded \(\kappa\)-fat open sets. Zbl 1266.60137Kim, Panki; Park, Hyunchul; Song, Renming 4 2013 Erratum to “Lévy risk model with two-sided jumps and a barrier dividend strategy”. Zbl 1291.91094Bo, Lijun; Song, Renming; Tang, Dan; Wang, Yongjin; Yang, Xuewei 1 2013 Bernstein functions. Theory and applications. 2nd revised and extended ed. Zbl 1257.33001Schilling, René L.; Song, Renming; Vondraček, Zoran 231 2012 Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation. Zbl 1264.60060Chen, Zhen-Qing; Kim, Panki; Song, Renming 55 2012 Sharp heat kernel estimates for relativistic stable processes in open sets. Zbl 1235.60101Chen, Zhen-Qing; Kim, Panki; Song, Renming 38 2012 Boundary Harnack principle for \(\Delta +\Delta ^{\alpha /2}\). Zbl 1271.31006Chen, Zhen-Qing; Kim, Panki; Song, Renming; Vondraček, Zoran 37 2012 Potential theory of subordinate Brownian motions revisited. Zbl 1282.60076Kim, Panki; Song, Renming; Vondraček, Zoran 36 2012 Two-sided Green function estimates for killed subordinate Brownian motions. Zbl 1248.60091Kim, Panki; Song, Renming; Vondraček, Zoran 29 2012 Uniform boundary Harnack principle for rotationally symmetric Lévy processes in general open sets. Zbl 1262.60077Kim, Panki; Song, RenMing; Vondraček, Zoran 22 2012 Global heat kernel estimate for relativistic stable processes in exterior open sets. Zbl 1255.60076Chen, Zhen-Qing; Kim, Panki; Song, Renming 17 2012 Global heat kernel estimates for relativistic stable processes in half-space-like open sets. Zbl 1239.60076Chen, Zhen-Qing; Kim, Panki; Song, Renming 12 2012 Lévy risk model with two-sided jumps and a barrier dividend strategy. Zbl 1244.91044Bo, 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 1247.60115Chen, Zhen-Qing; Kim, Panki; Song, Renming 6 2012 Minimal thinness for subordinate Brownian motion in half-space. Zbl 1273.60096Kim, Panki; Song, Renming; Vondraček, Zoran 4 2012 Heat kernel estimates for \(\Delta +\Delta ^{\alpha /2}\) in \(C^{1, 1}\) open sets. Zbl 1229.60089Chen, Zhen-Qing; Kim, Panki; Song, Renming 24 2011 Green function estimates for relativistic stable processes in half-space-like open sets. Zbl 1235.60100Chen, Zhen-Qing; Kim, Panki; Song, Renming 7 2011 \(L \log L\) condition for supercritical branching Hunt processes. Zbl 1215.60050Liu, Rong-Li; Ren, Yan-Xia; Song, Renming 7 2011 On harmonic functions for trace processes. Zbl 1227.60098Kim, Panki; Song, Renming; Vondraček, Zoran 4 2011 On the monitoring error of the supremum of a normal jump diffusion process. Zbl 1250.60036Chen, Ao; Feng, Liming; Song, Renming 3 2011 Selected works of Donald L. Burkholder. Edited by Burgess Davis and Renming Song. Zbl 1271.01046Burkholder, Donald L. 1 2011 Bernstein functions. Theory and applications. Zbl 1197.33002Schilling, René L.; Song, Renming; Vondraček, Zoran 134 2010 Heat kernel estimates for the Dirichlet fractional Laplacian. Zbl 1203.60114Chen, Zhen-Qing; Kim, Panki; Song, Renming 112 2010 Two-sided heat kernel estimates for censored stable-like processes. Zbl 1190.60068Chen, Zhen-Qing; Kim, Panki; Song, Renming 44 2010 Convexity and smoothness of scale functions and de Finetti’s control problem. Zbl 1188.93115Kyprianou, Andreas E.; Rivero, Víctor; Song, Renming 26 2010 Dirichlet heat kernel estimates for \(\Delta ^{\alpha /2} + \delta ^{\beta /2}\). Zbl 1268.60101Chen, Zhen-Qing; Kim, Panki; Song, Renming 26 2010 Sharp Green function estimates for \(\Delta + \delta ^{\alpha /2}\) in \(C^{1,1}\) open sets and their applications. Zbl 1257.31002Chen, Zhen-Qing; Kim, Panki; Song, Renming; Vondraček, Zoran 12 2010 On the potential theory of one-dimensional subordinate Brownian motions with continuous components. Zbl 1202.60125Kim, Panki; Song, Renming; Vondraček, Zoran 7 2010 Some remarks on special subordinators. Zbl 1196.60086Song, Renming; Vondraček, Zoran 3 2010 Boundary Harnack principle for subordinate Brownian motions. Zbl 1166.60046Kim, Panki; Song, Renming; Vondraček, Zoran 27 2009 Potential theory of subordinate Brownian motion. Zbl 1203.60118Song, R.; Vondraček, Z. 22 2009 \(L \log L\) criterion for a class of superdiffusions. Zbl 1175.60077Liu, Rong-Li; Ren, Yan-Xia; Song, Renming 19 2009 Intrinsic ultracontractivity for non-symmetric Lévy processes. Zbl 1175.47040Kim, Panki; Song, Renming 15 2009 Erratum to: “Intrinsic ultracontractivity for non-symmetric Lévy processes” [Forum Math. 21 (2009) 43-66]. Zbl 1179.47040Kim, Panki; Song, Renming 1 2009 A class of stochastic partial differential equations for interacting superprocesses on a bounded domain. Zbl 1170.60034Ren, Yan-Xia; Song, Renming; Wang, Hao 1 2009 Intrinsic ultracontractivity of non-symmetric diffusion semigroups in bounded domains. Zbl 1167.60017Kim, Panki; Song, Renming 23 2008 On the relationship between subordinate killed and killed subordinate processes. Zbl 1187.60057Song, Renming; Vondracek, Zoran 21 2008 Intrinsic ultracontractivity of nonsymmetric diffusions with measure-valued drifts and potentials. Zbl 1175.47039Kim, Panki; Song, Renming 13 2008 Boundary behavior of harmonic functions for truncated stable processes. Zbl 1145.60026Kim, Panki; Song, Renming 12 2008 On suprema of Lévy processes and application in risk theory. Zbl 1178.60036Song, Renming; Vondraček, Zoran 11 2008 On dual processes of non-symmetric diffusions with measure-valued drifts. Zbl 1146.60060Kim, Panki; Song, Renming 10 2008 Potential theory of truncated stable processes. Zbl 1115.60073Kim, Panki; Song, Renming 24 2007 Parabolic Harnack inequality for the mixture of Brownian motion and stable process. Zbl 1143.60049Song, Renming; Vondraček, Zoran 15 2007 ...and 40 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,323 Authors 95 Song, Renming 73 Chen, Zhen-Qing 71 Kim, Panki 34 Vondraček, Zoran 33 Wang, Jian 31 Ren, Yanxia 30 Qi, Feng 27 Duan, Jinqiao 23 Bogdan, Krzysztof 22 Kyprianou, Andreas E. 21 Schilling, René Leander 18 Grzywny, Tomasz 18 Kwaśnicki, Mateusz 16 Jakubowski, Tomasz 16 Kulczycki, Tadeusz 15 Guo, Bai-Ni 15 Kumagai, Takashi 15 Ryznar, Michał 15 Vazquez, Juan Luis 14 Kaleta, Kamil 14 Zhang, Xicheng 12 Chen, Huyuan 12 Mimica, Ante 12 Nane, Erkan 11 Lörinczi, József 10 Deng, Changsong 10 Kurths, Jürgen 10 Kuwae, Kazuhiro 10 Patie, Pierre 10 Ros-Oton, Xavier 10 Xie, Longjie 10 Xu, Wei 10 Zhang, Tusheng S. 9 Bañuelos, Rodrigo 9 Biswas, Anup 8 Ascione, Giacomo 8 Bass, Richard F. 8 Chen, Xin 8 Dipierro, Serena 8 Kim, KyeongHun 8 Li, Xiaofan 8 Mâagli, Habib 8 Park, Hyunchul 8 Sztonyk, Paweł 8 Tsuchida, Kaneharu 8 Valdinoci, Enrico 8 Zhang, Rui 7 Acuña Valverde, Luis 7 Beghin, Luisa 7 Bonforte, Matteo 7 Deng, Weihua 7 Grubb, Gerd 7 Kim, Daehong 7 Kühn, Franziska 7 Li, Lingfei 7 Linetsky, Vadim 7 Liu, Rongli 7 Małecki, Jacek 7 Menegatto, Valdir Antonio 7 Pardo, Juan Carlos 7 Sire, Yannick 7 Toaldo, Bruno 7 Yang, Xuewei 7 Yin, Chuancun 7 Zhang, Hongxia 6 Bazhlekova, Emilia G. 6 Caffarelli, Luis Ángel 6 D’Ovidio, Mirko 6 Foondun, Mohammud 6 Loeffen, Ronnie L. 6 Meerschaert, Mark Marvin 6 Mendoza-Arriaga, Rafael 6 Mugnai, Dimitri 6 Pietruska-Pałuba, Katarzyna 6 Porcu, Emilio 6 Sun, Zhenyao 6 Takeda, Masayoshi 6 Tawara, Yoshihiro 6 Yang, Ting 5 Cho, Soobin 5 Dyda, Bartłomiej 5 Hansen, Wolfhard 5 Hanyga, Andrzej 5 Harris, Simon C. 5 Jarohs, Sven 5 Karp, Dmitriĭ Borisovich 5 Kaßmann, Moritz 5 Kim, Ildoo 5 Leonenko, Nikolai N. 5 Luks, Tomasz 5 Mai, Jan-Frederik 5 Mainardi, Francesco 5 Metzler, Ralf 5 Pirozzi, Enrica 5 Siudeja, Bartłomiej Andrzej 5 Sun, Wei 5 Szczypkowski, Karol 5 Véron, Laurent 5 Wang, Feng-Yu 5 Wang, Jieming ...and 1,223 more Authors all top 5 Cited in 277 Serials 70 Potential Analysis 65 Stochastic Processes and their Applications 52 Journal of Functional Analysis 49 Journal of Mathematical Analysis and Applications 40 Transactions of the American Mathematical Society 38 Fractional Calculus & Applied Analysis 37 Journal of Differential Equations 36 Journal of Theoretical Probability 27 The Annals of Probability 24 Probability Theory and Related Fields 21 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 19 Statistics & Probability Letters 18 Proceedings of the American Mathematical Society 17 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 17 Electronic Journal of Probability 16 Bernoulli 14 Discrete and Continuous Dynamical Systems 14 Journal of Evolution Equations 13 Mathematische Nachrichten 12 Chaos, Solitons and Fractals 12 Mathematische Annalen 12 Science China. Mathematics 11 Journal of Statistical Physics 11 Mathematische Zeitschrift 10 Advances in Applied Probability 10 Communications in Mathematical Physics 10 Stochastics and Dynamics 10 ALEA. Latin American Journal of Probability and Mathematical Statistics 9 Applied Mathematics and Computation 9 Journal of Computational and Applied Mathematics 9 Journal of the London Mathematical Society. Second Series 9 The Annals of Applied Probability 9 The Journal of Geometric Analysis 9 Chaos 9 Communications in Nonlinear Science and Numerical Simulation 8 Journal of Mathematical Physics 8 Journal of Applied Probability 8 Stochastic Analysis and Applications 8 Journal de Mathématiques Pures et Appliquées. Neuvième Série 8 Journal of Physics A: Mathematical and Theoretical 7 Computers & Mathematics with Applications 7 Journal of Computational Physics 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Fuzzy Sets and Systems 7 Insurance Mathematics & Economics 7 Acta Applicandae Mathematicae 7 Forum Mathematicum 6 Studia Mathematica 6 Illinois Journal of Mathematics 6 Tôhoku Mathematical Journal. Second Series 6 Communications in Partial Differential Equations 6 Calculus of Variations and Partial Differential Equations 6 Discrete and Continuous Dynamical Systems. Series B 6 Mediterranean Journal of Mathematics 5 Nonlinearity 5 Physica A 5 Advances in Mathematics 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Results in Mathematics 5 Finance and Stochastics 5 Positivity 5 Acta Mathematica Sinica. English Series 5 Stochastics 5 Frontiers of Mathematics in China 5 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 4 Reviews in Mathematical Physics 4 Integral Equations and Operator Theory 4 Journal of the Mathematical Society of Japan 4 Applied Mathematics Letters 4 SIAM Journal on Mathematical Analysis 4 Theory of Probability and Mathematical Statistics 4 Filomat 4 Mathematical Finance 4 Mathematical Inequalities & Applications 4 Journal of the European Mathematical Society (JEMS) 4 Communications in Contemporary Mathematics 4 Communications on Pure and Applied Analysis 4 Analysis & PDE 4 Problemy Analiza. Issues of Analysis 4 Advances in Nonlinear Analysis 4 Dependence Modeling 4 Modern Stochastics. Theory and Applications 3 Archive for Rational Mechanics and Analysis 3 Journal d’Analyse Mathématique 3 Mathematical Notes 3 Journal of Approximation Theory 3 Journal of Optimization Theory and Applications 3 Memoirs of the American Mathematical Society 3 Proceedings of the London Mathematical Society. Third Series 3 Semigroup Forum 3 Revista Matemática Iberoamericana 3 Journal of Scientific Computing 3 Linear Algebra and its Applications 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 SIAM Journal on Scientific Computing 3 NoDEA. Nonlinear Differential Equations and Applications 3 Advances in Computational Mathematics 3 Electronic Communications in Probability 3 The Journal of Fourier Analysis and Applications 3 Journal of Inequalities and Applications ...and 177 more Serials all top 5 Cited in 46 Fields 808 Probability theory and stochastic processes (60-XX) 490 Partial differential equations (35-XX) 213 Operator theory (47-XX) 141 Real functions (26-XX) 139 Potential theory (31-XX) 75 Special functions (33-XX) 59 Statistical mechanics, structure of matter (82-XX) 56 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 55 Numerical analysis (65-XX) 54 Harmonic analysis on Euclidean spaces (42-XX) 47 Integral equations (45-XX) 47 Statistics (62-XX) 45 Functional analysis (46-XX) 41 Integral transforms, operational calculus (44-XX) 33 Ordinary differential equations (34-XX) 27 Dynamical systems and ergodic theory (37-XX) 27 Systems theory; control (93-XX) 24 Biology and other natural sciences (92-XX) 22 Functions of a complex variable (30-XX) 21 Global analysis, analysis on manifolds (58-XX) 18 Measure and integration (28-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 17 Combinatorics (05-XX) 17 Quantum theory (81-XX) 16 Number theory (11-XX) 13 Abstract harmonic analysis (43-XX) 12 Fluid mechanics (76-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 9 Approximations and expansions (41-XX) 8 Difference and functional equations (39-XX) 8 Mechanics of deformable solids (74-XX) 6 Operations research, mathematical programming (90-XX) 4 Sequences, series, summability (40-XX) 4 Differential geometry (53-XX) 4 Optics, electromagnetic theory (78-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Geophysics (86-XX) 2 Mathematical logic and foundations (03-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Convex and discrete geometry (52-XX) 2 Computer science (68-XX) 2 Information and communication theory, circuits (94-XX) 1 Algebraic geometry (14-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Manifolds and cell complexes (57-XX) Citations by Year