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Author ID: song.renming Recent zbMATH articles by "Song, Renming"
Published as: Song, Renming; Song, R.; Song, Ren Ming; Song, RenMing
Homepage: http://www.math.uiuc.edu/~rsong/
External Links: MGP · ORCID · ResearchGate · dblp · GND
Documents Indexed: 150 Publications since 1984, including 2 Books
2 Contributions as Editor
Reviewing Activity: 104 Reviews
Co-Authors: 57 Co-Authors with 141 Joint Publications
1,754 Co-Co-Authors
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Serials

14 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 Electronic Journal of Probability
5 Science China. Mathematics
4 Transactions of the American Mathematical Society
4 Acta Applicandae Mathematicae
4 Electronic Communications in Probability
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 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 Differential Equations
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

Publications by Year

Citations contained in zbMATH Open

133 Publications have been cited 2,194 times in 1,097 Documents Cited by Year
Bernstein functions. Theory and applications. 2nd revised and extended ed. Zbl 1257.33001
Schilling, René L.; Song, Renming; Vondraček, Zoran
154
2012
Estimates on Green functions and Poisson kernels for symmetric stable processes. Zbl 0918.60068
Chen, Zhen-Qing; Song, Renming
106
1998
Heat kernel estimates for the Dirichlet fractional Laplacian. Zbl 1203.60114
Chen, Zhen-Qing; Kim, Panki; Song, Renming
100
2010
Bernstein functions. Theory and applications. Zbl 1197.33002
Schilling, René L.; Song, Renming; Vondraček, Zoran
88
2010
Two-sided eigenvalue estimates for subordinate processes in domains. Zbl 1081.60056
Chen, Zhen-Qing; Song, Renming
68
2005
Intrinsic ultracontractivity and conditional gauge for symmetric stable processes. Zbl 0886.60072
Chen, Zhen-Qing; Song, Renming
61
1997
Drift transforms and Green function estimates for discontinuous processes. Zbl 1031.60071
Chen, Zhen-Qing; Song, Renming
56
2003
Potential theory of subordinate killed Brownian motion in a domain. Zbl 1022.60078
Song, Renming; Vondraček, Zoran
52
2003
Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation. Zbl 1264.60060
Chen, Zhen-Qing; Kim, Panki; Song, Renming
50
2012
Boundary Harnack principle for symmetric stable processes. Zbl 0945.31006
Song, Renming; Wu, Jang-Mei
48
1999
Harnack inequality for some classes of Markov processes. Zbl 1052.60064
Song, Renming; Vondraček, Zoran
46
2004
Mean exit time and escape probability for dynamical systems driven by Lévy noises. Zbl 1318.60065
Gao, T.; Duan, J.; Li, X.; Song, R.
43
2014
Two-sided heat kernel estimates for censored stable-like processes. Zbl 1190.60068
Chen, Zhen-Qing; Kim, Panki; Song, Renming
40
2010
General gauge and conditional gauge theorems. Zbl 1017.60086
Chen, Zhen-Qing; Song, Renming
37
2002
Sharp heat kernel estimates for relativistic stable processes in open sets. Zbl 1235.60101
Chen, Zhen-Qing; Kim, Panki; Song, Renming
37
2012
Global uniform boundary Harnack principle with explicit decay rate and its application. Zbl 1296.60198
Kim, Panki; Song, Renming; Vondraček, Zoran
37
2014
Conditional gauge theorem for non-local Feynman-Kac transforms. Zbl 1025.60032
Chen, Zhen-Qing; Song, Renming
36
2003
Green function estimates and Harnack inequality for subordinate Brownian motions. Zbl 1107.60042
Rao, Murali; Song, Renming; Vondraček, Zoran
34
2006
Martin boundary and integral representation for harmonic functions of symmetric stable processes. Zbl 0954.60003
Chen, Zhen-Qing; Song, Renming
31
1998
Two-sided estimates on the density of Brownian motion with singular drift. Zbl 1110.60071
Kim, Panki; Song, Renming
30
2006
Dirichlet heat kernel estimates for rotationally symmetric Lévy processes. Zbl 1304.60080
Chen, Zhen-Qing; Kim, Panki; Song, Renming
27
2014
Two-sided Green function estimates for killed subordinate Brownian motions. Zbl 1248.60091
Kim, Panki; Song, Renming; Vondraček, Zoran
27
2012
Boundary Harnack principle for subordinate Brownian motions. Zbl 1166.60046
Kim, Panki; Song, Renming; Vondraček, Zoran
27
2009
Boundary Harnack principle for \(\Delta +\Delta ^{\alpha /2}\). Zbl 1271.31006
Chen, Zhen-Qing; Kim, Panki; Song, Renming; Vondraček, Zoran
26
2012
Potential theory of truncated stable processes. Zbl 1115.60073
Kim, Panki; Song, Renming
24
2007
Hardy inequality for censored stable processes. Zbl 1070.46021
Chen, Zhen-Qing; Song, Renming
24
2003
Intrinsic ultracontractivity, conditional lifetimes and conditional gauge for symmetric stable processes on rough domains. Zbl 0959.60035
Chen, Zhen-Qing; Song, Renming
24
2000
Convexity and smoothness of scale functions and de Finetti’s control problem. Zbl 1188.93115
Kyprianou, Andreas E.; Rivero, Víctor; Song, Renming
23
2010
Potential theory of subordinate Brownian motions revisited. Zbl 1282.60076
Kim, Panki; Song, Renming; Vondraček, Zoran
23
2012
Dirichlet heat kernel estimates for \(\Delta ^{\alpha /2} + \delta ^{\beta /2}\). Zbl 1268.60101
Chen, Zhen-Qing; Kim, Panki; Song, Renming
22
2010
Uniform boundary Harnack principle for rotationally symmetric Lévy processes in general open sets. Zbl 1262.60077
Kim, Panki; Song, RenMing; Vondraček, Zoran
21
2012
Potential theory of special subordinators and subordinate killed stable processes. Zbl 1119.60063
Song, Renming; Vondraček, Zoran
20
2006
On the relationship between subordinate killed and killed subordinate processes. Zbl 1187.60057
Song, Renming; Vondracek, Zoran
20
2008
Intrinsic ultracontractivity of non-symmetric diffusion semigroups in bounded domains. Zbl 1167.60017
Kim, Panki; Song, Renming
20
2008
Heat kernels of non-symmetric jump processes: beyond the stable case. Zbl 1409.60116
Kim, Panki; Song, Renming; Vondraček, Zoran
19
2018
Potential theory of geometric stable processes. Zbl 1099.60051
Šikić, Hrvoje; Song, Renming; Vondraček, Zoran
19
2006
Stable process with singular drift. Zbl 1336.60112
Kim, Panki; Song, Renming
19
2014
A remark on diffusion of directed polymers in random environments. Zbl 0924.60053
Song, Renming; Zhou, Xian Yin
19
1996
Potential theory of subordinate Brownian motion. Zbl 1203.60118
Song, R.; Vondraček, Z.
19
2009
Heat kernel estimates for \(\Delta +\Delta ^{\alpha /2}\) in \(C^{1, 1}\) open sets. Zbl 1229.60089
Chen, Zhen-Qing; Kim, Panki; Song, Renming
19
2011
Potential theory of subordinate Brownian motions with Gaussian components. Zbl 1266.31007
Kim, Panki; Song, Renming; Vondraček, Zoran
18
2013
Stochastic flows for Lévy processes with Hölder drifts. Zbl 1420.60064
Chen, Zhen-Qing; Song, Renming; Zhang, Xicheng
17
2018
Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation. Zbl 1321.60149
Chen, Zhen-Qing; Kim, Panki; Song, Renming
17
2015
Global heat kernel estimate for relativistic stable processes in exterior open sets. Zbl 1255.60076
Chen, Zhen-Qing; Kim, Panki; Song, Renming
16
2012
Estimates on the Dirichlet heat kernel of domains above the graphs of bounded \(C^{1,1}\) functions. Zbl 1064.35066
Song, Renming
16
2004
Strong law of large numbers for a class of superdiffusions. Zbl 1260.60170
Liu, Rong-Li; Ren, Yan-Xia; Song, Renming
15
2013
Dirichlet heat kernel estimates for subordinate Brownian motions with Gaussian components. Zbl 1333.60179
Chen, Zhen-Qing; Kim, Panki; Song, Renming
14
2016
\(L \log L\) criterion for a class of superdiffusions. Zbl 1175.60077
Liu, Rong-Li; Ren, Yan-Xia; Song, Renming
14
2009
Sharp bounds on the density, Green function and jumping function of subordinate killed BM. Zbl 1054.60080
Song, Renming
14
2004
Parabolic Harnack inequality for the mixture of Brownian motion and stable process. Zbl 1143.60049
Song, Renming; Vondraček, Zoran
14
2007
Estimates on Green functions and Schrödinger-type equations for non-symmetric diffusions with measure-valued drifts. Zbl 1118.35007
Kim, Panki; Song, Renming
13
2007
Intrinsic ultracontractivity for non-symmetric Lévy processes. Zbl 1175.47040
Kim, Panki; Song, Renming
13
2009
Intrinsic ultracontractivity of nonsymmetric diffusions with measure-valued drifts and potentials. Zbl 1175.47039
Kim, Panki; Song, Renming
13
2008
Two-sided estimates on the density of the Feynman-Kac semigroups of stable-like processes. Zbl 1112.60059
Song, Renming
11
2006
Quasi-stationarity and quasi-ergodicity of general Markov processes. Zbl 1309.60078
Zhang, Junfei; Li, Shoumei; Song, Renming
11
2014
Quadratic forms corresponding to the generalized Schrödinger semigroups. Zbl 0807.60056
Glover, J.; Rao, M.; Šikić, H.; Song, R.
11
1994
Global heat kernel estimates for relativistic stable processes in half-space-like open sets. Zbl 1239.60076
Chen, Zhen-Qing; Kim, Panki; Song, Renming
11
2012
Harnack inequality for some discontinuous Markov processes with a diffusion part. Zbl 1075.60096
Song, Renming; Vondraček, Zoran
11
2005
Boundary behavior of harmonic functions for truncated stable processes. Zbl 1145.60026
Kim, Panki; Song, Renming
11
2008
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
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
11
2010
Central limit theorems for supercritical branching Markov processes. Zbl 1292.60034
Ren, Yan-Xia; Song, Renming; Zhang, Rui
10
2014
Continuity of eigenvalues of subordinate processes in domains. Zbl 1090.60070
Chen, Zhen-Qing; Song, Renming
10
2006
Central limit theorems for supercritical branching nonsymmetric Markov processes. Zbl 1365.60020
Ren, Yan-Xia; Song, Renming; Zhang, Rui
10
2017
Asymmetric non-Gaussian effects in a tumor growth model with immunization. Zbl 1428.92049
Hao, Mengli; Duan, Jinqiao; Song, Renming; Xu, Wei
9
2014
Feynman-Kac semigroup with discontinuous additive functionals. Zbl 0831.60085
Song, Renming
9
1995
On dual processes of non-symmetric diffusions with measure-valued drifts. Zbl 1146.60060
Kim, Panki; Song, Renming
9
2008
Application of Carleson’s theorem to wavelet inversion. Zbl 0816.42018
Rao, Murali; Šikić, Hrvoje; Song, Renming
8
1994
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
Trace estimates for relativistic stable processes. Zbl 1308.60059
Park, Hyunchul; Song, Renming
7
2014
Martin boundary for some symmetric Lévy processes. Zbl 1336.31031
Kim, Panki; Song, Renming; Vondraček, Zoran
7
2015
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
Diffusion of directed polymers in a strong random environment. Zbl 1081.82626
Olsen, Peder; Song, Renming
7
1996
Green function estimates for relativistic stable processes in half-space-like open sets. Zbl 1235.60100
Chen, Zhen-Qing; Kim, Panki; Song, Renming
7
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
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
7
2015
Central limit theorems for super Ornstein-Uhlenbeck processes. Zbl 1301.60027
Ren, Yan-Xia; Song, Renming; Zhang, Rui
7
2014
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
6
2018
Boundary Harnack principle and Martin boundary at infinity for subordinate Brownian motions. Zbl 1302.60110
Kim, Panki; Song, Renming; Vondraček, Zoran
6
2014
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
Probabilistic approach to the Dirichlet problem of perturbed stable processes. Zbl 0792.60067
Song, Renming
6
1993
Limit theorems for some critical superprocesses. Zbl 1338.60074
Ren, Yan-Xia; Song, Renming; Zhang, Rui
6
2015
Scale invariant boundary Harnack principle at infinity for Feller processes. Zbl 1381.60110
Kim, Panki; Song, Renming; Vondraček, Zoran
6
2017
Central limit theorems for supercritical superprocesses. Zbl 1325.60019
Ren, Yan-Xia; Song, Renming; Zhang, Rui
6
2015
Spectral heat content for Lévy processes. Zbl 1472.35209
Grzywny, Tomasz; Park, Hyunchul; Song, Renming
5
2019
Probabilistic methods in Schrödinger equations. Zbl 0691.60050
Ma, Zhiming; Song, Renming
5
1990
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
5
2019
Weak extinction versus global exponential growth of total mass for superdiffusions. Zbl 1341.60102
Engländer, János; Ren, Yan-Xia; Song, Renming
5
2016
Spine decompositions and limit theorems for a class of critical superprocesses. Zbl 1434.60250
Ren, Yan-Xia; Song, Renming; Sun, Zhenyao
5
2020
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
5
2020
Accessibility, martin boundary and minimal thinness for Feller processes in metric measure spaces. Zbl 1395.60094
Kim, Panki; Song, Renming; Vondraček, Zoran
4
2018
Potential theory of subordinate killed Brownian motion. Zbl 1450.60040
Kim, Panki; Song, Renming; Vondraček, Zoran
4
2019
Estimates on the transition densities of Girsanov transforms of symmetric stable processes. Zbl 1118.60067
Song, Renming
4
2006
Minimal thinness for subordinate Brownian motion in half-space. Zbl 1273.60096
Kim, Panki; Song, Renming; Vondraček, Zoran
4
2012
On harmonic functions for trace processes. Zbl 1227.60098
Kim, Panki; Song, Renming; Vondraček, Zoran
4
2011
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
\(\Gamma\)-potentials. Zbl 0873.60052
Glover, Joseph; Rao, Murali; Šikić, Hrvoje; Song, Renming
4
1994
Homogenization of nonlocal partial differential equations related to stochastic differential equations with Lévy noise. Zbl 07526601
Huang, Qiao; Duan, Jinqiao; Song, Renming
1
2022
Spectral heat content for \(\alpha \)-stable processes in \({C^{1,1}}\) open sets. Zbl 1486.60066
Park, Hyunchul; Song, Renming
1
2022
The extremal process of super-Brownian motion. Zbl 1469.60260
Ren, Yan-Xia; Song, Renming; Zhang, Rui
2
2021
Spine decompositions and limit theorems for a class of critical superprocesses. Zbl 1434.60250
Ren, Yan-Xia; Song, Renming; Sun, Zhenyao
5
2020
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
5
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
3
2020
Well-posedness and long time behavior of singular Langevin stochastic differential equations. Zbl 1457.60102
Song, Renming; Xie, Longjie
2
2020
Gradient estimates for the fundamental solution of Lévy type operator. Zbl 1434.60207
Liu, Wei; Song, Renming; Xie, Longjie
2
2020
Limit theorems for a class of critical superprocesses with stable branching. Zbl 1434.60235
Ren, Yan-Xia; Song, Renming; Sun, Zhenyao
2
2020
On the boundary theory of subordinate killed Lévy processes. Zbl 1451.60090
Kim, Panki; Song, Renming; Vondraček, Zoran
2
2020
Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradients. Zbl 1468.60096
Song, Renming; Xie, Longjie; Xie, Yingchao
1
2020
Spectral heat content for Lévy processes. Zbl 1472.35209
Grzywny, Tomasz; Park, Hyunchul; Song, Renming
5
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
5
2019
Potential theory of subordinate killed Brownian motion. Zbl 1450.60040
Kim, Panki; Song, Renming; Vondraček, Zoran
4
2019
Stable central limit theorems for super Ornstein-Uhlenbeck processes. Zbl 1428.60120
Ren, 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 1420.60105
Chen, Zhen-Qing; Ren, Yan-Xia; Song, Renming
2
2019
Heat kernel estimates for Dirichlet fractional Laplacian with gradient perturbation. Zbl 1408.60069
Chen, Peng; Song, Renming; Xie, Longjie; Xie, Yingchao
1
2019
Supercritical superprocesses: proper normalization and non-degenerate strong limit. Zbl 1420.60102
Ren, Yan-Xia; Song, Renming; Zhang, Rui
1
2019
FSEM: functional structural equation models for twin functional data. Zbl 1418.62121
Luo, S.; Song, R.; Styner, M.; Gilmore, J. H.; Zhu, H.
1
2019
Heat kernels of non-symmetric jump processes: beyond the stable case. Zbl 1409.60116
Kim, Panki; Song, Renming; Vondraček, Zoran
19
2018
Stochastic flows for Lévy processes with Hölder drifts. Zbl 1420.60064
Chen, Zhen-Qing; Song, Renming; Zhang, Xicheng
17
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
6
2018
Accessibility, martin boundary and minimal thinness for Feller processes in metric measure spaces. Zbl 1395.60094
Kim, Panki; Song, Renming; Vondraček, Zoran
4
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
1
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
10
2017
Scale invariant boundary Harnack principle at infinity for Feller processes. Zbl 1381.60110
Kim, Panki; Song, Renming; Vondraček, Zoran
6
2017
Functional central limit theorems for supercritical superprocesses. Zbl 1370.60059
Ren, Yan-Xia; Song, Renming; Zhang, Rui
2
2017
Dirichlet heat kernel estimates for subordinate Brownian motions with Gaussian components. Zbl 1333.60179
Chen, Zhen-Qing; Kim, Panki; Song, Renming
14
2016
Weak extinction versus global exponential growth of total mass for superdiffusions. Zbl 1341.60102
Engländer, János; Ren, Yan-Xia; Song, Renming
5
2016
Minimal thinness with respect to subordinate killed Brownian motions. Zbl 1336.60160
Kim, Panki; Song, Renming; Vondraček, Zoran
4
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
2
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
17
2015
Martin boundary for some symmetric Lévy processes. Zbl 1336.31031
Kim, Panki; Song, Renming; Vondraček, Zoran
7
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
7
2015
Limit theorems for some critical superprocesses. Zbl 1338.60074
Ren, Yan-Xia; Song, Renming; Zhang, Rui
6
2015
Central limit theorems for supercritical superprocesses. Zbl 1325.60019
Ren, Yan-Xia; Song, Renming; Zhang, Rui
6
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.
43
2014
Global uniform boundary Harnack principle with explicit decay rate and its application. Zbl 1296.60198
Kim, Panki; Song, Renming; Vondraček, Zoran
37
2014
Dirichlet heat kernel estimates for rotationally symmetric Lévy processes. Zbl 1304.60080
Chen, Zhen-Qing; Kim, Panki; Song, Renming
27
2014
Stable process with singular drift. Zbl 1336.60112
Kim, Panki; Song, Renming
19
2014
Quasi-stationarity and quasi-ergodicity of general Markov processes. Zbl 1309.60078
Zhang, Junfei; Li, Shoumei; Song, Renming
11
2014
Central limit theorems for supercritical branching Markov processes. Zbl 1292.60034
Ren, Yan-Xia; Song, Renming; Zhang, Rui
10
2014
Asymmetric non-Gaussian effects in a tumor growth model with immunization. Zbl 1428.92049
Hao, Mengli; Duan, Jinqiao; Song, Renming; Xu, Wei
9
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
Central limit theorems for super Ornstein-Uhlenbeck processes. Zbl 1301.60027
Ren, Yan-Xia; Song, Renming; Zhang, Rui
7
2014
Boundary Harnack principle and Martin boundary at infinity for subordinate Brownian motions. Zbl 1302.60110
Kim, Panki; Song, Renming; Vondraček, Zoran
6
2014
Potential theory of subordinate Brownian motions with Gaussian components. Zbl 1266.31007
Kim, Panki; Song, Renming; Vondraček, Zoran
18
2013
Strong law of large numbers for a class of superdiffusions. Zbl 1260.60170
Liu, Rong-Li; Ren, Yan-Xia; Song, Renming
15
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
154
2012
Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation. Zbl 1264.60060
Chen, Zhen-Qing; Kim, Panki; Song, Renming
50
2012
Sharp heat kernel estimates for relativistic stable processes in open sets. Zbl 1235.60101
Chen, Zhen-Qing; Kim, Panki; Song, Renming
37
2012
Two-sided Green function estimates for killed subordinate Brownian motions. Zbl 1248.60091
Kim, Panki; Song, Renming; Vondraček, Zoran
27
2012
Boundary Harnack principle for \(\Delta +\Delta ^{\alpha /2}\). Zbl 1271.31006
Chen, Zhen-Qing; Kim, Panki; Song, Renming; Vondraček, Zoran
26
2012
Potential theory of subordinate Brownian motions revisited. Zbl 1282.60076
Kim, Panki; Song, Renming; Vondraček, Zoran
23
2012
Uniform boundary Harnack principle for rotationally symmetric Lévy processes in general open sets. Zbl 1262.60077
Kim, Panki; Song, RenMing; Vondraček, Zoran
21
2012
Global heat kernel estimate for relativistic stable processes in exterior open sets. Zbl 1255.60076
Chen, Zhen-Qing; Kim, Panki; Song, Renming
16
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
11
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
Minimal thinness for subordinate Brownian motion in half-space. Zbl 1273.60096
Kim, Panki; Song, Renming; Vondraček, Zoran
4
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
2
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
19
2011
Green function estimates for relativistic stable processes in half-space-like open sets. Zbl 1235.60100
Chen, Zhen-Qing; Kim, Panki; Song, Renming
7
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
4
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.
1
2011
Heat kernel estimates for the Dirichlet fractional Laplacian. Zbl 1203.60114
Chen, Zhen-Qing; Kim, Panki; Song, Renming
100
2010
Bernstein functions. Theory and applications. Zbl 1197.33002
Schilling, René L.; Song, Renming; Vondraček, Zoran
88
2010
Two-sided heat kernel estimates for censored stable-like processes. Zbl 1190.60068
Chen, Zhen-Qing; Kim, Panki; Song, Renming
40
2010
Convexity and smoothness of scale functions and de Finetti’s control problem. Zbl 1188.93115
Kyprianou, Andreas E.; Rivero, Víctor; Song, Renming
23
2010
Dirichlet heat kernel estimates for \(\Delta ^{\alpha /2} + \delta ^{\beta /2}\). Zbl 1268.60101
Chen, Zhen-Qing; Kim, Panki; Song, Renming
22
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
11
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
27
2009
Potential theory of subordinate Brownian motion. Zbl 1203.60118
Song, R.; Vondraček, Z.
19
2009
\(L \log L\) criterion for a class of superdiffusions. Zbl 1175.60077
Liu, Rong-Li; Ren, Yan-Xia; Song, Renming
14
2009
Intrinsic ultracontractivity for non-symmetric Lévy processes. Zbl 1175.47040
Kim, Panki; Song, Renming
13
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
1
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
On the relationship between subordinate killed and killed subordinate processes. Zbl 1187.60057
Song, Renming; Vondracek, Zoran
20
2008
Intrinsic ultracontractivity of non-symmetric diffusion semigroups in bounded domains. Zbl 1167.60017
Kim, Panki; Song, Renming
20
2008
Intrinsic ultracontractivity of nonsymmetric diffusions with measure-valued drifts and potentials. Zbl 1175.47039
Kim, Panki; Song, Renming
13
2008
Boundary behavior of harmonic functions for truncated stable processes. Zbl 1145.60026
Kim, Panki; Song, Renming
11
2008
On suprema of Lévy processes and application in risk theory. Zbl 1178.60036
Song, Renming; Vondraček, Zoran
11
2008
On dual processes of non-symmetric diffusions with measure-valued drifts. Zbl 1146.60060
Kim, Panki; Song, Renming
9
2008
Potential theory of truncated stable processes. Zbl 1115.60073
Kim, Panki; Song, Renming
24
2007
Parabolic Harnack inequality for the mixture of Brownian motion and stable process. Zbl 1143.60049
Song, Renming; Vondraček, Zoran
14
2007
Estimates on Green functions and Schrödinger-type equations for non-symmetric diffusions with measure-valued drifts. Zbl 1118.35007
Kim, Panki; Song, Renming
13
2007
Boundary Harnack principle for Brownian motions with measure-valued drifts in bounded Lipschitz domains. Zbl 1140.60038
Kim, Panki; Song, Renming
8
2007
Spectral properties of subordinate processes in domains. Zbl 1124.60059
Chen, Zhenqing; Song, Renming
1
2007
Green function estimates and Harnack inequality for subordinate Brownian motions. Zbl 1107.60042
Rao, Murali; Song, Renming; Vondraček, Zoran
34
2006
Two-sided estimates on the density of Brownian motion with singular drift. Zbl 1110.60071
Kim, Panki; Song, Renming
30
2006
Potential theory of special subordinators and subordinate killed stable processes. Zbl 1119.60063
Song, Renming; Vondraček, Zoran
20
2006
Potential theory of geometric stable processes. Zbl 1099.60051
Šikić, Hrvoje; Song, Renming; Vondraček, Zoran
19
2006
...and 33 more Documents
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Cited by 1,090 Authors

88 Song, Renming
70 Chen, Zhen-Qing
67 Kim, Panki
32 Wang, Jian
31 Vondraček, Zoran
28 Ren, Yanxia
26 Duan, Jinqiao
23 Bogdan, Krzysztof
20 Kyprianou, Andreas E.
17 Grzywny, Tomasz
16 Kulczycki, Tadeusz
16 Kwaśnicki, Mateusz
15 Jakubowski, Tomasz
15 Kumagai, Takashi
15 Qi, Feng
15 Ryznar, Michał
14 Vazquez, Juan Luis
13 Schilling, René Leander
12 Chen, Huyuan
12 Kaleta, Kamil
11 Mimica, Ante
11 Nane, Erkan
11 Zhang, Xicheng
10 Kurths, Jürgen
10 Kuwae, Kazuhiro
10 Lörinczi, József
9 Guo, Bai-Ni
9 Ros-Oton, Xavier
9 Xie, Longjie
8 Bañuelos, Rodrigo
8 Bass, Richard F.
8 Chen, Xin
8 Li, Xiaofan
8 Mâagli, Habib
8 Sztonyk, Paweł
8 Tsuchida, Kaneharu
8 Zhang, Rui
8 Zhang, Tusheng S.
7 Biswas, Anup
7 Deng, Weihua
7 Kim, Daehong
7 Kim, KyeongHun
7 Li, Lingfei
7 Małecki, Jacek
7 Pardo, Juan Carlos
7 Patie, Pierre
7 Sire, Yannick
7 Yang, Xuewei
7 Yin, Chuancun
6 Acuña Valverde, Luis
6 Ascione, Giacomo
6 Bonforte, Matteo
6 Caffarelli, Luis Ángel
6 Deng, Changsong
6 Dipierro, Serena
6 D’Ovidio, Mirko
6 Foondun, Mohammud
6 Linetsky, Vadim
6 Liu, Rongli
6 Loeffen, Ronnie L.
6 Meerschaert, Mark Marvin
6 Menegatto, Valdir Antonio
6 Park, Hyunchul
6 Pietruska-Pałuba, Katarzyna
6 Tawara, Yoshihiro
6 Valdinoci, Enrico
6 Xu, Wei
6 Yang, Ting
6 Zhang, Hongxia
5 Dyda, Bartłomiej
5 Grubb, Gerd
5 Hansen, Wolfhard
5 Hanyga, Andrzej
5 Harris, Simon C.
5 Jarohs, Sven
5 Kaßmann, Moritz
5 Kim, Ildoo
5 Kühn, Franziska
5 Leonenko, Nikolai N.
5 Luks, Tomasz
5 Mendoza-Arriaga, Rafael
5 Pirozzi, Enrica
5 Takeda, Masayoshi
5 Toaldo, Bruno
5 Véron, Laurent
5 Wang, Xiao
5 Yoshida, Nobuo
5 Zhao, GuoHuan
4 Bachar, Imed
4 Bazhlekova, Emilia G.
4 Beghin, Luisa
4 Bo, Lijun
4 Cho, Soobin
4 da Silva, José Luís
4 Duo, Siwei
4 Fahrenwaldt, Matthias Albrecht
4 Fall, Mouhamed Moustapha
4 Fitzsimmons, Patrick J.
4 He, Guoman
4 Kamocki, Rafal
...and 990 more Authors
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Cited in 239 Serials

65 Potential Analysis
58 Stochastic Processes and their Applications
46 Journal of Functional Analysis
41 Journal of Mathematical Analysis and Applications
40 Transactions of the American Mathematical Society
32 Journal of Theoretical Probability
29 Journal of Differential Equations
25 The Annals of Probability
22 Probability Theory and Related Fields
20 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
20 Fractional Calculus & Applied Analysis
17 Proceedings of the American Mathematical Society
16 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
15 Statistics & Probability Letters
13 Discrete and Continuous Dynamical Systems
12 Mathematische Annalen
12 Bernoulli
12 Science China. Mathematics
11 Journal of Statistical Physics
11 Mathematische Zeitschrift
11 Journal of Evolution Equations
10 Electronic Journal of Probability
10 Stochastics and Dynamics
9 The Annals of Applied Probability
9 Chaos
8 Communications in Mathematical Physics
8 The Journal of Geometric Analysis
8 Journal de Mathématiques Pures et Appliquées. Neuvième Série
8 Communications in Nonlinear Science and Numerical Simulation
7 Advances in Applied Probability
7 Computers & Mathematics with Applications
7 Chaos, Solitons and Fractals
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 Stochastic Analysis and Applications
7 Acta Applicandae Mathematicae
6 Journal of Mathematical Physics
6 ZAMP. Zeitschrift für angewandte Mathematik und Physik
6 Applied Mathematics and Computation
6 Illinois Journal of Mathematics
6 Tôhoku Mathematical Journal. Second Series
6 Forum Mathematicum
6 Communications in Partial Differential Equations
6 Discrete and Continuous Dynamical Systems. Series B
6 ALEA. Latin American Journal of Probability and Mathematical Statistics
5 Journal of Computational Physics
5 Advances in Mathematics
5 Annali di Matematica Pura ed Applicata. Serie Quarta
5 Calculus of Variations and Partial Differential Equations
5 Finance and Stochastics
5 Positivity
5 Acta Mathematica Sinica. English Series
5 Mediterranean Journal of Mathematics
5 Frontiers of Mathematics in China
5 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
4 Nonlinearity
4 Physica A
4 Studia Mathematica
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 Applied Mathematics Letters
4 Theory of Probability and Mathematical Statistics
4 The Journal of Fourier Analysis and Applications
4 Mathematical Finance
4 Journal of the European Mathematical Society (JEMS)
4 Communications in Contemporary Mathematics
4 Analysis & PDE
4 Problemy Analiza. Issues of Analysis
4 Advances in Nonlinear Analysis
3 Archive for Rational Mechanics and Analysis
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 Mathematical Analysis
3 SIAM Journal on Scientific Computing
3 Filomat
3 NoDEA. Nonlinear Differential Equations and Applications
3 Advances in Computational Mathematics
3 Electronic Communications in Probability
3 Journal of Inequalities and Applications
3 Infinite Dimensional Analysis, Quantum Probability and Related Topics
3 Stochastic Models
3 Advanced Nonlinear Studies
3 Communications on Pure and Applied Analysis
3 Journal of Physics A: Mathematical and Theoretical
3 Discrete and Continuous Dynamical Systems. Series S
3 Modern Stochastics. Theory and Applications
2 Applicable Analysis
2 Communications on Pure and Applied Mathematics
2 Journal d’Analyse Mathématique
...and 139 more Serials
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Cited in 45 Fields

691 Probability theory and stochastic processes (60-XX)
400 Partial differential equations (35-XX)
172 Operator theory (47-XX)
133 Potential theory (31-XX)
100 Real functions (26-XX)
52 Statistical mechanics, structure of matter (82-XX)
51 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
48 Special functions (33-XX)
46 Harmonic analysis on Euclidean spaces (42-XX)
45 Numerical analysis (65-XX)
42 Integral equations (45-XX)
36 Functional analysis (46-XX)
35 Statistics (62-XX)
29 Integral transforms, operational calculus (44-XX)
23 Ordinary differential equations (34-XX)
22 Systems theory; control (93-XX)
21 Dynamical systems and ergodic theory (37-XX)
19 Global analysis, analysis on manifolds (58-XX)
16 Measure and integration (28-XX)
15 Calculus of variations and optimal control; optimization (49-XX)
15 Biology and other natural sciences (92-XX)
14 Functions of a complex variable (30-XX)
14 Quantum theory (81-XX)
11 Combinatorics (05-XX)
11 Number theory (11-XX)
10 Abstract harmonic analysis (43-XX)
9 Fluid mechanics (76-XX)
7 Difference and functional equations (39-XX)
7 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 Sequences, series, summability (40-XX)
4 Differential geometry (53-XX)
4 Optics, electromagnetic theory (78-XX)
4 Classical thermodynamics, heat transfer (80-XX)
4 Geophysics (86-XX)
3 Several complex variables and analytic spaces (32-XX)
2 Computer science (68-XX)
1 Mathematical logic and foundations (03-XX)
1 Algebraic geometry (14-XX)
1 Nonassociative rings and algebras (17-XX)
1 Convex and discrete geometry (52-XX)
1 Manifolds and cell complexes (57-XX)
1 Information and communication theory, circuits (94-XX)

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