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## Song, Renming

Compute Distance To:
 Author ID: song.renming Published as: Song, Renming; Song, R.; Song, RenMing Homepage: http://www.math.uiuc.edu/~rsong/ External Links: MGP · ORCID · ResearchGate · dblp · GND
 Documents Indexed: 143 Publications since 1984, including 2 Books Reviewing Activity: 97 Reviews
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#### Co-Authors

 10 single-authored 48 Kim, Panki 38 Vondraček, Zoran 30 Chen, Zhen-Qing 21 Ren, Yanxia 10 Zhang, Rui 8 Rao, Murali 7 Glover, Joseph 5 Šikić, Hrvoje 5 Sun, Zhenyao 4 Liu, Rongli 4 Park, Hyunchul 4 Xie, Longjie 3 Duan, Jinqiao 3 Ma, Zhi-Ming 2 Bo, Lijun 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 1 Chen, Ao 1 Chen, Peng 1 Cho, Soobin 1 Engländer, János 1 Feng, Liming 1 Fitzsimmons, Patrick J. 1 Gao, Ting 1 Gilmore, John H. 1 Grzywny, Tomasz 1 Hao, Mengli 1 Herrell, Randall 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 Styner, Martin A. 1 Wang, Hao 1 Wang, Xiao 1 Wu, Dongsheng 1 Wu, Jang-Mei 1 Xu, Wei 1 Yang, Xiaochuan 1 Zhang, Junfei 1 Zhang, Xicheng 1 Zhao, Jianjie 1 Zhou, Xianyin 1 Zhu, Hongtu
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#### Serials

 13 Stochastic Processes and their Applications 10 Potential Analysis 9 Journal of Functional Analysis 9 Probability Theory and Related Fields 7 Journal of Theoretical 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 Journal of Probability 4 Electronic Communications in Probability 3 Mathematische Zeitschrift 3 Tohoku Mathematical Journal. Second Series 3 Acta Mathematicae Applicatae Sinica. English Series 3 Forum Mathematicum 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 Journal of Mathematical Analysis and Applications 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 American Statistical Association 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 Journal of the European Mathematical Society (JEMS) 1 Frontiers of Mathematics in China 1 Advances in Nonlinear Analysis
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#### Fields

 132 Probability theory and stochastic processes (60-XX) 30 Potential theory (31-XX) 26 Operator theory (47-XX) 15 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 Special functions (33-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Numerical analysis (65-XX) 1 History and biography (01-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)

#### Citations contained in zbMATH Open

117 Publications have been cited 1,881 times in 906 Documents Cited by Year
Bernstein functions. Theory and applications. 2nd revised and extended ed. Zbl 1257.33001
Schilling, René L.; Song, Renming; Vondraček, Zoran
2012
Estimates on Green functions and Poisson kernels for symmetric stable processes. Zbl 0918.60068
Chen, Zhen-Qing; Song, Renming
1998
Heat kernel estimates for the Dirichlet fractional Laplacian. Zbl 1203.60114
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2010
Bernstein functions. Theory and applications. Zbl 1197.33002
Schilling, René L.; Song, Renming; Vondraček, Zoran
2010
Intrinsic ultracontractivity and conditional gauge for symmetric stable processes. Zbl 0886.60072
Chen, Zhen-Qing; Song, Renming
1997
Two-sided eigenvalue estimates for subordinate processes in domains. Zbl 1081.60056
Chen, Zhen-Qing; Song, Renming
2005
Drift transforms and Green function estimates for discontinuous processes. Zbl 1031.60071
Chen, Zhen-Qing; Song, Renming
2003
Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation. Zbl 1264.60060
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2012
Harnack inequality for some classes of Markov processes. Zbl 1052.60064
Song, Renming; Vondraček, Zoran
2004
Boundary Harnack principle for symmetric stable processes. Zbl 0945.31006
Song, Renming; Wu, Jang-Mei
1999
Potential theory of subordinate killed Brownian motion in a domain. Zbl 1022.60078
Song, Renming; Vondraček, Zoran
2003
General gauge and conditional gauge theorems. Zbl 1017.60086
Chen, Zhen-Qing; Song, Renming
2002
Sharp heat kernel estimates for relativistic stable processes in open sets. Zbl 1235.60101
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2012
Two-sided heat kernel estimates for censored stable-like processes. Zbl 1190.60068
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2010
Mean exit time and escape probability for dynamical systems driven by Lévy noises. Zbl 1318.60065
Gao, T.; Duan, J.; Li, X.; Song, R.
2014
Global uniform boundary Harnack principle with explicit decay rate and its application. Zbl 1296.60198
Kim, Panki; Song, Renming; Vondraček, Zoran
2014
Conditional gauge theorem for non-local Feynman-Kac transforms. Zbl 1025.60032
Chen, Zhen-Qing; Song, Renming
2003
Martin boundary and integral representation for harmonic functions of symmetric stable processes. Zbl 0954.60003
Chen, Zhen-Qing; Song, Renming
1998
Green function estimates and Harnack inequality for subordinate Brownian motions. Zbl 1107.60042
Rao, Murali; Song, Renming; Vondraček, Zoran
2006
Two-sided estimates on the density of Brownian motion with singular drift. Zbl 1110.60071
Kim, Panki; Song, Renming
2006
Boundary Harnack principle for subordinate Brownian motions. Zbl 1166.60046
Kim, Panki; Song, Renming; Vondraček, Zoran
2009
Two-sided Green function estimates for killed subordinate Brownian motions. Zbl 1248.60091
Kim, Panki; Song, Renming; Vondraček, Zoran
2012
Intrinsic ultracontractivity, conditional lifetimes and conditional gauge for symmetric stable processes on rough domains. Zbl 0959.60035
Chen, Zhen-Qing; Song, Renming
2000
Potential theory of truncated stable processes. Zbl 1115.60073
Kim, Panki; Song, Renming
2007
Convexity and smoothness of scale functions and de Finetti’s control problem. Zbl 1188.93115
Kyprianou, Andreas E.; Rivero, Víctor; Song, Renming
2010
Dirichlet heat kernel estimates for rotationally symmetric Lévy processes. Zbl 1304.60080
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2014
Hardy inequality for censored stable processes. Zbl 1070.46021
Chen, Zhen-Qing; Song, Renming
2003
Dirichlet heat kernel estimates for $$\Delta ^{\alpha /2} + \delta ^{\beta /2}$$. Zbl 1268.60101
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2010
Potential theory of subordinate Brownian motions revisited. Zbl 1282.60076
Kim, Panki; Song, Renming; Vondraček, Zoran
2012
Potential theory of special subordinators and subordinate killed stable processes. Zbl 1119.60063
Song, Renming; Vondraček, Zoran
2006
Potential theory of subordinate Brownian motion. Zbl 1203.60118
Song, R.; Vondraček, Z.
2009
Uniform boundary Harnack principle for rotationally symmetric Lévy processes in general open sets. Zbl 1262.60077
Kim, Panki; Song, RenMing; Vondraček, Zoran
2012
Intrinsic ultracontractivity of non-symmetric diffusion semigroups in bounded domains. Zbl 1167.60017
Kim, Panki; Song, Renming
2008
A remark on diffusion of directed polymers in random environments. Zbl 0924.60053
Song, Renming; Zhou, Xian Yin
1996
On the relationship between subordinate killed and killed subordinate processes. Zbl 1187.60057
Song, Renming; Vondracek, Zoran
2008
Boundary Harnack principle for $$\Delta +\Delta ^{\alpha /2}$$. Zbl 1271.31006
Chen, Zhen-Qing; Kim, Panki; Song, Renming; Vondraček, Zoran
2012
Potential theory of subordinate Brownian motions with Gaussian components. Zbl 1266.31007
Kim, Panki; Song, Renming; Vondraček, Zoran
2013
Stable process with singular drift. Zbl 1336.60112
Kim, Panki; Song, Renming
2014
Potential theory of geometric stable processes. Zbl 1099.60051
Šikić, Hrvoje; Song, Renming; Vondraček, Zoran
2006
Strong law of large numbers for a class of superdiffusions. Zbl 1260.60170
Liu, Rong-Li; Ren, Yan-Xia; Song, Renming
2013
Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation. Zbl 1321.60149
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2015
Global heat kernel estimate for relativistic stable processes in exterior open sets. Zbl 1255.60076
Chen, Zhen-Qing; Kim, Panki; Song, Renming
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
2011
$$L \log L$$ criterion for a class of superdiffusions. Zbl 1175.60077
Liu, Rong-Li; Ren, Yan-Xia; Song, Renming
2009
Estimates on the Dirichlet heat kernel of domains above the graphs of bounded $$C^{1,1}$$ functions. Zbl 1064.35066
Song, Renming
2004
Heat kernels of non-symmetric jump processes: beyond the stable case. Zbl 1409.60116
Kim, Panki; Song, Renming; Vondraček, Zoran
2018
Intrinsic ultracontractivity of nonsymmetric diffusions with measure-valued drifts and potentials. Zbl 1175.47039
Kim, Panki; Song, Renming
2008
Intrinsic ultracontractivity for non-symmetric Lévy processes. Zbl 1175.47040
Kim, Panki; Song, Renming
2009
Estimates on Green functions and Schrödinger-type equations for non-symmetric diffusions with measure-valued drifts. Zbl 1118.35007
Kim, Panki; Song, Renming
2007
Stochastic flows for Lévy processes with Hölder drifts. Zbl 1420.60064
Chen, Zhen-Qing; Song, Renming; Zhang, Xicheng
2018
On suprema of Lévy processes and application in risk theory. Zbl 1178.60036
Song, Renming; Vondraček, Zoran
2008
Quadratic forms corresponding to the generalized Schrödinger semigroups. Zbl 0807.60056
Glover, J.; Rao, M.; Šikić, H.; Song, R.
1994
Parabolic Harnack inequality for the mixture of Brownian motion and stable process. Zbl 1143.60049
Song, Renming; Vondraček, Zoran
2007
Boundary behavior of harmonic functions for truncated stable processes. Zbl 1145.60026
Kim, Panki; Song, Renming
2008
Sharp bounds on the density, Green function and jumping function of subordinate killed BM. Zbl 1054.60080
Song, Renming
2004
Dirichlet heat kernel estimates for subordinate Brownian motions with Gaussian components. Zbl 1333.60179
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2016
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
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
2012
Feynman-Kac semigroup with discontinuous additive functionals. Zbl 0831.60085
Song, Renming
1995
Harnack inequality for some discontinuous Markov processes with a diffusion part. Zbl 1075.60096
Song, Renming; Vondraček, Zoran
2005
On dual processes of non-symmetric diffusions with measure-valued drifts. Zbl 1146.60060
Kim, Panki; Song, Renming
2008
Quasi-stationarity and quasi-ergodicity of general Markov processes. Zbl 1309.60078
Zhang, Junfei; Li, Shoumei; Song, Renming
2014
Continuity of eigenvalues of subordinate processes in domains. Zbl 1090.60070
Chen, Zhen-Qing; Song, Renming
2006
Central limit theorems for supercritical branching Markov processes. Zbl 1292.60034
Ren, Yan-Xia; Song, Renming; Zhang, Rui
2014
Boundary Harnack principle for Brownian motions with measure-valued drifts in bounded Lipschitz domains. Zbl 1140.60038
Kim, Panki; Song, Renming
2007
On the (N) fuzzy integral. Zbl 0641.28014
Song, Renming
1985
Central limit theorems for supercritical branching nonsymmetric Markov processes. Zbl 1365.60020
Ren, Yan-Xia; Song, Renming; Zhang, Rui
2017
$$L \log L$$ condition for supercritical branching Hunt processes. Zbl 1215.60050
Liu, Rong-Li; Ren, Yan-Xia; Song, Renming
2011
On the potential theory of one-dimensional subordinate Brownian motions with continuous components. Zbl 1202.60125
Kim, Panki; Song, Renming; Vondraček, Zoran
2010
Application of Carleson’s theorem to wavelet inversion. Zbl 0816.42018
Rao, Murali; Šikić, Hrvoje; Song, Renming
1994
Martin boundary for some symmetric Lévy processes. Zbl 1336.31031
Kim, Panki; Song, Renming; Vondraček, Zoran
2015
Green function estimates for relativistic stable processes in half-space-like open sets. Zbl 1235.60100
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2011
Two-sided estimates on the density of the Feynman-Kac semigroups of stable-like processes. Zbl 1112.60059
Song, Renming
2006
Asymmetric non-Gaussian effects in a tumor growth model with immunization. Zbl 1428.92049
Hao, Mengli; Duan, Jinqiao; Song, Renming; Xu, Wei
2014
Probabilistic approach to the Dirichlet problem of perturbed stable processes. Zbl 0792.60067
Song, Renming
1993
Harmonic functions of subordinate killed Brownian motion. Zbl 1061.60077
Glover, J.; Pop-Stojanovic, Z.; Rao, M.; Šikić, H.; Song, R.; Vondraček, Z.
2004
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
2015
Central limit theorems for super Ornstein-Uhlenbeck processes. Zbl 1301.60027
Ren, Yan-Xia; Song, Renming; Zhang, Rui
2014
Limit theorems for some critical superprocesses. Zbl 1338.60074
Ren, Yan-Xia; Song, Renming; Zhang, Rui
2015
Diffusion of directed polymers in a strong random environment. Zbl 1081.82626
Olsen, Peder; Song, Renming
1996
Scale invariant boundary Harnack principle at infinity for Feller processes. Zbl 1381.60110
Kim, Panki; Song, Renming; Vondraček, Zoran
2017
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
2010
Trace estimates for relativistic stable processes. Zbl 1308.60059
Park, Hyunchul; Song, Renming
2014
Boundary Harnack principle and Martin boundary at infinity for subordinate Brownian motions. Zbl 1302.60110
Kim, Panki; Song, Renming; Vondraček, Zoran
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
2014
Central limit theorems for supercritical superprocesses. Zbl 1325.60019
Ren, Yan-Xia; Song, Renming; Zhang, Rui
2015
Weak extinction versus global exponential growth of total mass for superdiffusions. Zbl 1341.60102
Engländer, János; Ren, Yan-Xia; Song, Renming
2016
Probabilistic methods in Schrödinger equations. Zbl 0691.60050
Ma, Zhiming; Song, Renming
1990
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
2018
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
2013
Estimates on the transition densities of Girsanov transforms of symmetric stable processes. Zbl 1118.60067
Song, Renming
2006
Minimal thinness for subordinate Brownian motion in half-space. Zbl 1273.60096
Kim, Panki; Song, Renming; Vondraček, Zoran
2012
On the monitoring error of the supremum of a normal jump diffusion process. Zbl 1250.60036
Chen, Ao; Feng, Liming; Song, Renming
2011
Some remarks on special subordinators. Zbl 1196.60086
Song, Renming; Vondraček, Zoran
2010
$$\Gamma$$-potentials. Zbl 0873.60052
Glover, Joseph; Rao, Murali; Šikić, Hrvoje; Song, Renming
1994
Minimal thinness with respect to subordinate killed Brownian motions. Zbl 1336.60160
Kim, Panki; Song, Renming; Vondraček, Zoran
2016
Minimal thinness with respect to symmetric Lévy processes. Zbl 1356.60074
Kim, Panki; Song, Renming; Vondraček, Zoran
2016
Crossing estimates for symmetric Markov processes. Zbl 0994.31004
Chen, Z.-Q.; Fitzsimmons, P. J.; Song, R.
2001
On harmonic functions for trace processes. Zbl 1227.60098
Kim, Panki; Song, Renming; Vondraček, Zoran
2011
$$L \log L$$ criterion for a class of multitype superdiffusions with non-local branching mechanisms. Zbl 1420.60105
Chen, Zhen-Qing; Ren, Yan-Xia; Song, Renming
2019
Spine decompositions and limit theorems for a class of critical superprocesses. Zbl 1434.60250
Ren, Yan-Xia; Song, Renming; Sun, Zhenyao
2020
Limit theorems for a class of critical superprocesses with stable branching. Zbl 1434.60235
Ren, Yan-Xia; Song, Renming; Sun, Zhenyao
2020
$$L \log L$$ criterion for a class of multitype superdiffusions with non-local branching mechanisms. Zbl 1420.60105
Chen, Zhen-Qing; Ren, Yan-Xia; Song, Renming
2019
Potential theory of subordinate killed Brownian motion. Zbl 1450.60040
Kim, Panki; Song, Renming; Vondraček, Zoran
2019
Stable central limit theorems for super Ornstein-Uhlenbeck processes. Zbl 1428.60120
Ren, Yan-Xia; Song, Renming; Sun, Zhenyao; Zhao, Jianjie
2019
Supercritical superprocesses: proper normalization and non-degenerate strong limit. Zbl 1420.60102
Ren, Yan-Xia; Song, Renming; Zhang, Rui
2019
Heat kernel estimates for Dirichlet fractional Laplacian with gradient perturbation. Zbl 1408.60069
Chen, Peng; Song, Renming; Xie, Longjie; Xie, Yingchao
2019
Heat kernels of non-symmetric jump processes: beyond the stable case. Zbl 1409.60116
Kim, Panki; Song, Renming; Vondraček, Zoran
2018
Stochastic flows for Lévy processes with Hölder drifts. Zbl 1420.60064
Chen, Zhen-Qing; Song, Renming; Zhang, Xicheng
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
2018
Accessibility, martin boundary and minimal thinness for Feller processes in metric measure spaces. Zbl 1395.60094
Kim, Panki; Song, Renming; Vondraček, Zoran
2018
Uniform Hausdorff dimension result for the inverse images of stable Lévy processes. Zbl 1398.60089
Song, Renming; Xiao, Yimin; Yang, Xiaochuan
2018
Central limit theorems for supercritical branching nonsymmetric Markov processes. Zbl 1365.60020
Ren, Yan-Xia; Song, Renming; Zhang, Rui
2017
Scale invariant boundary Harnack principle at infinity for Feller processes. Zbl 1381.60110
Kim, Panki; Song, Renming; Vondraček, Zoran
2017
Functional central limit theorems for supercritical superprocesses. Zbl 1370.60059
Ren, Yan-Xia; Song, Renming; Zhang, Rui
2017
Dirichlet heat kernel estimates for subordinate Brownian motions with Gaussian components. Zbl 1333.60179
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2016
Weak extinction versus global exponential growth of total mass for superdiffusions. Zbl 1341.60102
Engländer, János; Ren, Yan-Xia; Song, Renming
2016
Minimal thinness with respect to subordinate killed Brownian motions. Zbl 1336.60160
Kim, Panki; Song, Renming; Vondraček, Zoran
2016
Minimal thinness with respect to symmetric Lévy processes. Zbl 1356.60074
Kim, Panki; Song, Renming; Vondraček, Zoran
2016
Martin boundary of unbounded sets for purely discontinuous Feller processes. Zbl 1351.60106
Kim, Panki; Song, Renming; Vondraček, Zoran
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
2015
Martin boundary for some symmetric Lévy processes. Zbl 1336.31031
Kim, Panki; Song, Renming; Vondraček, Zoran
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
2015
Limit theorems for some critical superprocesses. Zbl 1338.60074
Ren, Yan-Xia; Song, Renming; Zhang, Rui
2015
Central limit theorems for supercritical superprocesses. Zbl 1325.60019
Ren, Yan-Xia; Song, Renming; Zhang, Rui
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.
2014
Global uniform boundary Harnack principle with explicit decay rate and its application. Zbl 1296.60198
Kim, Panki; Song, Renming; Vondraček, Zoran
2014
Dirichlet heat kernel estimates for rotationally symmetric Lévy processes. Zbl 1304.60080
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2014
Stable process with singular drift. Zbl 1336.60112
Kim, Panki; Song, Renming
2014
Quasi-stationarity and quasi-ergodicity of general Markov processes. Zbl 1309.60078
Zhang, Junfei; Li, Shoumei; Song, Renming
2014
Central limit theorems for supercritical branching Markov processes. Zbl 1292.60034
Ren, Yan-Xia; Song, Renming; Zhang, Rui
2014
Asymmetric non-Gaussian effects in a tumor growth model with immunization. Zbl 1428.92049
Hao, Mengli; Duan, Jinqiao; Song, Renming; Xu, Wei
2014
Central limit theorems for super Ornstein-Uhlenbeck processes. Zbl 1301.60027
Ren, Yan-Xia; Song, Renming; Zhang, Rui
2014
Trace estimates for relativistic stable processes. Zbl 1308.60059
Park, Hyunchul; Song, Renming
2014
Boundary Harnack principle and Martin boundary at infinity for subordinate Brownian motions. Zbl 1302.60110
Kim, Panki; Song, Renming; Vondraček, Zoran
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
2014
Potential theory of subordinate Brownian motions with Gaussian components. Zbl 1266.31007
Kim, Panki; Song, Renming; Vondraček, Zoran
2013
Strong law of large numbers for a class of superdiffusions. Zbl 1260.60170
Liu, Rong-Li; Ren, Yan-Xia; Song, Renming
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
2013
Bernstein functions. Theory and applications. 2nd revised and extended ed. Zbl 1257.33001
Schilling, René L.; Song, Renming; Vondraček, Zoran
2012
Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation. Zbl 1264.60060
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2012
Sharp heat kernel estimates for relativistic stable processes in open sets. Zbl 1235.60101
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2012
Two-sided Green function estimates for killed subordinate Brownian motions. Zbl 1248.60091
Kim, Panki; Song, Renming; Vondraček, Zoran
2012
Potential theory of subordinate Brownian motions revisited. Zbl 1282.60076
Kim, Panki; Song, Renming; Vondraček, Zoran
2012
Uniform boundary Harnack principle for rotationally symmetric Lévy processes in general open sets. Zbl 1262.60077
Kim, Panki; Song, RenMing; Vondraček, Zoran
2012
Boundary Harnack principle for $$\Delta +\Delta ^{\alpha /2}$$. Zbl 1271.31006
Chen, Zhen-Qing; Kim, Panki; Song, Renming; Vondraček, Zoran
2012
Global heat kernel estimate for relativistic stable processes in exterior open sets. Zbl 1255.60076
Chen, Zhen-Qing; Kim, Panki; Song, Renming
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
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
2012
Minimal thinness for subordinate Brownian motion in half-space. Zbl 1273.60096
Kim, Panki; Song, Renming; Vondraček, Zoran
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
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
2011
$$L \log L$$ condition for supercritical branching Hunt processes. Zbl 1215.60050
Liu, Rong-Li; Ren, Yan-Xia; Song, Renming
2011
Green function estimates for relativistic stable processes in half-space-like open sets. Zbl 1235.60100
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2011
On the monitoring error of the supremum of a normal jump diffusion process. Zbl 1250.60036
Chen, Ao; Feng, Liming; Song, Renming
2011
On harmonic functions for trace processes. Zbl 1227.60098
Kim, Panki; Song, Renming; Vondraček, Zoran
2011
Heat kernel estimates for the Dirichlet fractional Laplacian. Zbl 1203.60114
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2010
Bernstein functions. Theory and applications. Zbl 1197.33002
Schilling, René L.; Song, Renming; Vondraček, Zoran
2010
Two-sided heat kernel estimates for censored stable-like processes. Zbl 1190.60068
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2010
Convexity and smoothness of scale functions and de Finetti’s control problem. Zbl 1188.93115
Kyprianou, Andreas E.; Rivero, Víctor; Song, Renming
2010
Dirichlet heat kernel estimates for $$\Delta ^{\alpha /2} + \delta ^{\beta /2}$$. Zbl 1268.60101
Chen, Zhen-Qing; Kim, Panki; Song, Renming
2010
On the potential theory of one-dimensional subordinate Brownian motions with continuous components. Zbl 1202.60125
Kim, Panki; Song, Renming; Vondraček, Zoran
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
2010
Some remarks on special subordinators. Zbl 1196.60086
Song, Renming; Vondraček, Zoran
2010
Boundary Harnack principle for subordinate Brownian motions. Zbl 1166.60046
Kim, Panki; Song, Renming; Vondraček, Zoran
2009
Potential theory of subordinate Brownian motion. Zbl 1203.60118
Song, R.; Vondraček, Z.
2009
$$L \log L$$ criterion for a class of superdiffusions. Zbl 1175.60077
Liu, Rong-Li; Ren, Yan-Xia; Song, Renming
2009
Intrinsic ultracontractivity for non-symmetric Lévy processes. Zbl 1175.47040
Kim, Panki; Song, Renming
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
2009
Erratum to: “Intrinsic ultracontractivity for non-symmetric Lévy processes” [Forum Math. 21 (2009) 43-66]. Zbl 1179.47040
Kim, Panki; Song, Renming
2009
Intrinsic ultracontractivity of non-symmetric diffusion semigroups in bounded domains. Zbl 1167.60017
Kim, Panki; Song, Renming
2008
On the relationship between subordinate killed and killed subordinate processes. Zbl 1187.60057
Song, Renming; Vondracek, Zoran
2008
Intrinsic ultracontractivity of nonsymmetric diffusions with measure-valued drifts and potentials. Zbl 1175.47039
Kim, Panki; Song, Renming
2008
On suprema of Lévy processes and application in risk theory. Zbl 1178.60036
Song, Renming; Vondraček, Zoran
2008
Boundary behavior of harmonic functions for truncated stable processes. Zbl 1145.60026
Kim, Panki; Song, Renming
2008
On dual processes of non-symmetric diffusions with measure-valued drifts. Zbl 1146.60060
Kim, Panki; Song, Renming
2008
Potential theory of truncated stable processes. Zbl 1115.60073
Kim, Panki; Song, Renming
2007
Estimates on Green functions and Schrödinger-type equations for non-symmetric diffusions with measure-valued drifts. Zbl 1118.35007
Kim, Panki; Song, Renming
2007
Parabolic Harnack inequality for the mixture of Brownian motion and stable process. Zbl 1143.60049
Song, Renming; Vondraček, Zoran
2007
Boundary Harnack principle for Brownian motions with measure-valued drifts in bounded Lipschitz domains. Zbl 1140.60038
Kim, Panki; Song, Renming
2007
Spectral properties of subordinate processes in domains. Zbl 1124.60059
Chen, Zhenqing; Song, Renming
2007
Green function estimates and Harnack inequality for subordinate Brownian motions. Zbl 1107.60042
Rao, Murali; Song, Renming; Vondraček, Zoran
2006
Two-sided estimates on the density of Brownian motion with singular drift. Zbl 1110.60071
Kim, Panki; Song, Renming
2006
Potential theory of special subordinators and subordinate killed stable processes. Zbl 1119.60063
Song, Renming; Vondraček, Zoran
2006
Potential theory of geometric stable processes. Zbl 1099.60051
Šikić, Hrvoje; Song, Renming; Vondraček, Zoran
2006
Continuity of eigenvalues of subordinate processes in domains. Zbl 1090.60070
Chen, Zhen-Qing; Song, Renming
2006
Two-sided estimates on the density of the Feynman-Kac semigroups of stable-like processes. Zbl 1112.60059
Song, Renming
2006
Estimates on the transition densities of Girsanov transforms of symmetric stable processes. Zbl 1118.60067
Song, Renming
2006
Two-sided eigenvalue estimates for subordinate processes in domains. Zbl 1081.60056
Chen, Zhen-Qing; Song, Renming
2005
Harnack inequality for some discontinuous Markov processes with a diffusion part. Zbl 1075.60096
Song, Renming; Vondraček, Zoran
2005
Harnack inequality for some classes of Markov processes. Zbl 1052.60064
Song, Renming; Vondraček, Zoran
2004
Estimates on the Dirichlet heat kernel of domains above the graphs of bounded $$C^{1,1}$$ functions. Zbl 1064.35066
Song, Renming
2004
Sharp bounds on the density, Green function and jumping function of subordinate killed BM. Zbl 1054.60080
Song, Renming
2004
Harmonic functions of subordinate killed Brownian motion. Zbl 1061.60077
Glover, J.; Pop-Stojanovic, Z.; Rao, M.; Šikić, H.; Song, R.; Vondraček, Z.
2004
Sharp bounds for Green functions and jumping functions of subordinate killed Brownian motions in bounded $$C^ {1,1}$$ domains. Zbl 1060.60078
Song, Renming; Vondraček, Zoran
2004
Drift transforms and Green function estimates for discontinuous processes. Zbl 1031.60071
Chen, Zhen-Qing; Song, Renming
2003
Potential theory of subordinate killed Brownian motion in a domain. Zbl 1022.60078
Song, Renming; Vondraček, Zoran
2003
Conditional gauge theorem for non-local Feynman-Kac transforms. Zbl 1025.60032
Chen, Zhen-Qing; Song, Renming
2003
Hardy inequality for censored stable processes. Zbl 1070.46021
Chen, Zhen-Qing; Song, Renming
2003
General gauge and conditional gauge theorems. Zbl 1017.60086
Chen, Zhen-Qing; Song, Renming
2002
...and 17 more Documents
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#### Cited by 900 Authors

 83 Song, Renming 62 Chen, Zhen-Qing 62 Kim, Panki 30 Vondraček, Zoran 25 Ren, Yanxia 23 Duan, Jinqiao 22 Bogdan, Krzysztof 22 Wang, Jian 16 Kulczycki, Tadeusz 16 Kyprianou, Andreas E. 15 Grzywny, Tomasz 15 Ryznar, Michał 14 Kwaśnicki, Mateusz 13 Jakubowski, Tomasz 12 Chen, Huyuan 12 Schilling, René Leander 11 Kumagai, Takashi 11 Mimica, Ante 11 Vazquez, Juan Luis 10 Kaleta, Kamil 10 Nane, Erkan 10 Zhang, Xicheng 9 Kurths, Jürgen 9 Kuwae, Kazuhiro 9 Lörinczi, József 8 Bañuelos, Rodrigo 8 Bass, Richard F. 8 Li, Xiaofan 8 Mâagli, Habib 8 Qi, Feng 8 Tsuchida, Kaneharu 8 Xie, Longjie 8 Zhang, Rui 7 Li, Lingfei 7 Małecki, Jacek 7 Pardo, Juan Carlos 7 Ros-Oton, Xavier 7 Sztonyk, Paweł 7 Yang, Xuewei 7 Yin, Chuancun 7 Zhang, Tusheng S. 6 Biswas, Anup 6 Bonforte, Matteo 6 Caffarelli, Luis Ángel 6 Chen, Xin 6 Foondun, Mohammud 6 Kim, Daehong 6 Kim, KyeongHun 6 Linetsky, Vadim 6 Meerschaert, Mark Marvin 6 Tawara, Yoshihiro 5 Acuña Valverde, Luis 5 D’Ovidio, Mirko 5 Grubb, Gerd 5 Guo, Bai-Ni 5 Hansen, Wolfhard 5 Hanyga, Andrzej 5 Jarohs, Sven 5 Kassmann, Moritz 5 Kim, Ildoo 5 Lee, Ki-Ahm 5 Liu, Rongli 5 Loeffen, Ronnie L. 5 Mendoza-Arriaga, Rafael 5 Takeda, Masayoshi 5 Véron, Laurent 5 Wang, Xiao 5 Yang, Ting 5 Yoshida, Nobuo 4 Bachar, Imed 4 Bazhlekova, Emilia G. 4 Bo, Lijun 4 da Silva, José Luís 4 Deng, Changsong 4 Deng, Weihua 4 Duo, Siwei 4 Dyda, Bartłomiej 4 Fahrenwaldt, Matthias Albrecht 4 Kondrat’yev, Yuriĭ Grygorovych 4 Leonenko, Nikolai N. 4 Luks, Tomasz 4 Lv, Guangying 4 Méndez-Hernández, Pedro J. 4 Menegatto, Valdir Antonio 4 Mugnai, Dimitri 4 Palau, Sandra 4 Patie, Pierre 4 Pietruska-Pałuba, Katarzyna 4 Porcu, Emilio 4 Rao, Murali 4 Shiozawa, Yuichi 4 Sire, Yannick 4 Siudeja, Bartłomiej Andrzej 4 Sun, Wei 4 Toaldo, Bruno 4 Wang, Feng-Yu 4 Yuen, Kam Chuen 4 Zheng, Yayun 4 Zhigljavsky, Anatoly A. 3 Abatangelo, Nicola ...and 800 more Authors
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#### Cited in 202 Serials

 62 Potential Analysis 51 Stochastic Processes and their Applications 44 Journal of Functional Analysis 39 Journal of Mathematical Analysis and Applications 33 Transactions of the American Mathematical Society 30 Journal of Theoretical Probability 22 Journal of Differential Equations 21 The Annals of Probability 19 Probability Theory and Related Fields 18 Fractional Calculus & Applied Analysis 15 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 15 Proceedings of the American Mathematical Society 14 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 12 Bernoulli 12 Science China. Mathematics 11 Statistics & Probability Letters 11 Discrete and Continuous Dynamical Systems 10 Journal of Statistical Physics 10 Mathematische Annalen 9 Chaos 9 Journal of Evolution Equations 9 Stochastics and Dynamics 8 Mathematische Zeitschrift 8 Electronic Journal of Probability 7 Computers & Mathematics with Applications 7 Communications in Mathematical Physics 7 Fuzzy Sets and Systems 7 Journal of Applied Probability 7 Journal of Computational and Applied Mathematics 7 Mathematische Nachrichten 7 Insurance Mathematics & Economics 7 The Annals of Applied Probability 6 Journal of Mathematical Physics 6 Applied Mathematics and Computation 6 Illinois Journal of Mathematics 6 Tohoku Mathematical Journal. Second Series 6 Stochastic Analysis and Applications 6 Acta Applicandae Mathematicae 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Communications in Nonlinear Science and Numerical Simulation 6 Discrete and Continuous Dynamical Systems. Series B 5 Advances in Applied Probability 5 Journal of Computational Physics 5 Communications in Partial Differential Equations 5 Finance and Stochastics 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Reviews in Mathematical Physics 4 Integral Equations and Operator Theory 4 Journal of the London Mathematical Society. Second Series 4 Journal of the Mathematical Society of Japan 4 Forum Mathematicum 4 Calculus of Variations and Partial Differential Equations 4 Mathematical Finance 4 Journal of the European Mathematical Society (JEMS) 4 Acta Mathematica Sinica. English Series 4 Mediterranean Journal of Mathematics 4 Frontiers of Mathematics in China 4 Advances in Nonlinear Analysis 3 Nonlinearity 3 Studia Mathematica 3 Chaos, Solitons and Fractals 3 Advances in Mathematics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Proceedings of the London Mathematical Society. Third Series 3 Semigroup Forum 3 Revista Matemática Iberoamericana 3 Applied Mathematics Letters 3 The Journal of Geometric Analysis 3 Linear Algebra and its Applications 3 SIAM Journal on Scientific Computing 3 Advances in Computational Mathematics 3 The Journal of Fourier Analysis and Applications 3 Infinite Dimensional Analysis, Quantum Probability and Related Topics 3 Communications in Contemporary Mathematics 3 Stochastic Models 3 Advanced Nonlinear Studies 3 Communications on Pure and Applied Analysis 3 ALEA. Latin American Journal of Probability and Mathematical Statistics 3 Analysis & PDE 3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 3 Problemy Analiza. Issues of Analysis 3 Modern Stochastics. Theory and Applications 2 Archive for Rational Mechanics and Analysis 2 Communications on Pure and Applied Mathematics 2 Journal d’Analyse Mathématique 2 Mathematical Notes 2 Rocky Mountain Journal of Mathematics 2 Archiv der Mathematik 2 Duke Mathematical Journal 2 Journal of Approximation Theory 2 Journal of Optimization Theory and Applications 2 Manuscripta Mathematica 2 Operations Research 2 Quarterly of Applied Mathematics 2 Probability and Mathematical Statistics 2 Acta Mathematica Hungarica 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Constructive Approximation 2 Journal of Scientific Computing 2 SIAM Journal on Mathematical Analysis ...and 102 more Serials
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#### Cited in 43 Fields

 592 Probability theory and stochastic processes (60-XX) 317 Partial differential equations (35-XX) 151 Operator theory (47-XX) 122 Potential theory (31-XX) 66 Real functions (26-XX) 47 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 36 Integral equations (45-XX) 36 Statistical mechanics, structure of matter (82-XX) 35 Harmonic analysis on Euclidean spaces (42-XX) 34 Numerical analysis (65-XX) 28 Statistics (62-XX) 27 Functional analysis (46-XX) 25 Special functions (33-XX) 21 Systems theory; control (93-XX) 20 Integral transforms, operational calculus (44-XX) 18 Dynamical systems and ergodic theory (37-XX) 16 Measure and integration (28-XX) 16 Ordinary differential equations (34-XX) 16 Global analysis, analysis on manifolds (58-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 9 Functions of a complex variable (30-XX) 9 Abstract harmonic analysis (43-XX) 9 Fluid mechanics (76-XX) 9 Quantum theory (81-XX) 7 Combinatorics (05-XX) 7 Biology and other natural sciences (92-XX) 6 Number theory (11-XX) 6 Approximations and expansions (41-XX) 6 Mechanics of deformable solids (74-XX) 6 Operations research, mathematical programming (90-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 4 Geophysics (86-XX) 3 Sequences, series, summability (40-XX) 3 Differential geometry (53-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Difference and functional equations (39-XX) 2 Optics, electromagnetic theory (78-XX) 1 Mathematical logic and foundations (03-XX) 1 Algebraic geometry (14-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX) 1 Information and communication theory, circuits (94-XX)