List of Publications

  1. R. Song: Regular fuzzy numbers. J. Hebei Univ., (Natural Sci. Ed.), Vol. 3, No. 2 (1983), 86-87.

  2. R. Song: On the extension of a class of fuzzy measures. J. Hebei Univ., (Natural Sci. Ed.), Vol. 4, No. 2 (1984), 97-101.

  3. R. Song: On the (N)--fuzzy integral. Fuzzy Math., Vol. 5. No. 3 (1985), 91-106.

  4. Q. Yang and R. Song: Further discussion of the pan-integral on fuzzy measure spaces. Fuzzy Math., Vol. 5. No. 4 (1985), 27-36.

  5. Z. Li and R. Song: Probabilistic representations of the solutions to the Schrodinger equations. Chin. J. of Appl. Probab. Stat., Vol. 2, No. 1 (1986), 66--70.

  6. R. Song: A note on fuzzy measures of fuzzy subsets. Fuzzy Math., Vol. 6, No. 3 (1986), 13-14.

  7. Z. Ma and R. Song: Probabilistic approach to Neumann Problem with infinite gauge. Acta Math. Appl. Sinica, Vol. 4 (1988), 30--40. PDF

  8. R. Song: Probabilistic approach to the Dirichlet problem of second order elliptic PDE. Acta Math. Appl. Sinica, Vol. 5 (1989), 137--147. PDF

  9. R. Song: Probabilistic approach to the Dirichlet problem of a class of semilinear equations. Chin. J. Appl. Probab. Stat., Vol. 5, No. 1 (1989), 61--69.

  10. R. Song: Probabilistic approach to the third boundary value problem. J. of Hebei Univ., (Natural Sci. Ed.), Vol. 9, No. 1 (1989), 85--100.

  11. R. Song: On a class of special Markov processes. J. Hebei Univ., (Natural Sci. Ed.), Vol. 9, No. 3 (1989), 1-8.

  12. Z. Ma and R. Song: Probabilistic methods in Schrodinger equations. Seminar on Stochastic Processes, 1989 (edited by E. Cinlar, K. L. Chung and R. K. Getoor), Birkhauser, Boston, 1990, 135-164.

  13. J. Glover and R. Song: Multiplicative symmetry groups of Markov processes. Seminar on Stochastic Processes, 1990 (edited by E. Cinlar, K. L. Chung and R. K. Getoor), Birkhauser, Boston, 1991, 193-206.

  14. Z. Ma and R. Song: Probabilistic approach to semilinear and generalized mixed boundary value problems. Acta Math. Appl. Sinica, Vol. 8, No.3 (1992), 214--228. PDF

  15. J. Glover, M. Rao and R. Song: Generalized Schrodinger semigroups. Seminar on Stochastic Processes, 1992 (edited by E. Cinlar, K. L. Chung and M. J. Sharpe), Birkhauser, Boston, 1993, 143-172.

  16. J. Glover, M. Rao and R. Song: The gauge theorem for a class of additive functionals of zero energy. Probab. Th. rel. Fields, Vol. 97 (1993), 195-210. PDF

  17. R. Song: Probabilistic approach to the Dirichlet problem of perturbed stable processes. Probab. Th. rel. Fields, Vol. 95 (1993), 371--389. PDF

  18. J. Glover, M. Rao, H. Sikic and R. Song: $\Gamma$-potentials. Classical and Modern Potential Theory and Applications (edited by K. GowriSankaran et al), Kluwer Academic Publishers, Dordrechet, Netherlands, 1994, 217-232. PDF

  19. M. Rao, H. Sikic and R. Song: Application of Carleson's theorem to wavelet inversions. Control and Cybern. Vol. 23 (1994), 761-771. PDF

  20. J. Glover, M. Rao, H. Sikic and R. Song: Quadratic forms corresponding to the generalized Schrodinger semigroup. J. Funct. Anal., Vol. 125 (1994), 358-378. PDF

  21. R. Song: Feynman-Kac semigroups with discontinuous additive functionals. J. Theor. Probab., Vol. 8 (1995), 727-762. PDF

  22. P. Olsen and R. Song: Diffusion of directed polymers in a strong random environment. J. Stat. Physics, Vol. 83 (1996), 727-738. PDF

  23. R. Song and X. Y. Zhou: A remark on diffusion of directed polymers in random environments. J. Stat. Physics, Vol. 85 (1996), 277-289. PDF

  24. Z.-Q. Chen and R. Song: Intrinsic ultracontractivity and conditional gauge for symmetric stable processes. J. Funct. Anal., Vol. 150 (1997), 204-239. PDF

  25. Z.-Q. Chen and R. Song: Estimates on the Green functions and Poisson kernels of symmetric stable processes. Math. Ann., Vol. 312 (1998), 465-501. PDF

  26. Z.-Q. Chen and R. Song: Martin boundary and integral representation for harmonic functions of symmetric stable processes. J. of Funct. Anal., Vol. 159 (1998), 267-294. PDF

  27. J. Conlon and R. Song: Gaussian limit theorems for diffusion processes and an application. Stoch. Proc. Appl., Vol. 81 (1999), 103--128.

  28. R. Song and J.-M. Wu: Boundary Harnack inequality for symmetric stable processes. J. of Funct. Anal., Vol. 168 (1999), 403-427. PDF

  29. Z.-Q. Chen and R. Song: Intrinsic ultracontractivity, conditional lifetimes and conditional gauge for symmetric stable processes on rough domains. Illinois J. Math., Vol. 44 (2000), 138-160. PDF

  30. J. Conlon and R. Song: Random Walks associated with non divergence form elliptic equations. J. Theor. Probab., Vol. 13 (2000), 427-489.

  31. Z.-Q. Chen, P. J. Fitzsimmons and R. Song: Crossing Estimates for Symmetric Markov Processes. Probab. Th. rel. Fields, Vol. 120 (2001), 68-84. PDF

  32. Z.-Q. Chen and R. Song: General gauge and conditional gauge theorems. Ann. Probab., Vol. 30 (2002), 1313-1339. PDF

  33. S. Albeverio, R. Song and X. Y. Zhou: On the partition function and diffusive behavior of directed polymers in a random environment. Collections Papers of Zhou Xianyin, Beijing Normal University Press, Beijing, 2002. 911-914.

  34. Z.-Q. Chen and R. Song: Conditional gauge theorems for non-local Feynman-Kac transforms. Probab. Theory Related Fields, Vol. 125, No. 1 (2003), 45--72. PDF

  35. Z.-Q. Chen and R. Song: Drift transforms and Green function estimates for discontinuous processes. J. Funct. Anal. Vol. 201, No. 1 (2003), 262--281. PDF

  36. Z.-Q. Chen and R. Song: Hardy inequality for censored stable processes. Tohoko Math. J., Vol. 55(2003), 439-450. PDF

  37. R. Song and Z. Vondracek: Potential theory of subordinate killed Brownian motion in a domain. Probab. Theory Related Fields, Vol. 125, No.4 (2003), 578--592. PDF

  38. R. Song and Z. Vondracek: Harnack inequality for some classes of Markov processes. Math. Z. Vol. 246, No. 1-2 (2004), 177--202. PDF

  39. Z.-Q. Chen and R. Song: A note on the Green function estimates for symmetric stable processes. Recent developments in stochastic analysis and related topics, (Proceedings of the First Sino-German Conference on Stochastic Analysis), 125--135, World Sci. Publ., Hackensack, NJ, 2004. Postscript PDF

  40. R. Song: Sharp bounds on the density, Green function and Jumping function of subordinate killed BM. Probab. Theory Related Fields, Vol. 128, No. 4 (2004), 606--628. PDF

  41. R. Song: Estimates on the Dirichlet heat kernel of domains above the graphs of bounded $C^{1, 1}$ functions. Glas. Mat., Vol. 39, No. 2 (2004), 273--286. Postscript PDF

  42. J. Glover, M. Rao, Z. Pop-Stojanovic, H Sikic, R. Song and Z. Vondracek: Harmonic functions of subordinate killed Brownian motions. J. Funct. Anal., Vol. 215, NO. 2 (2004), 399--426. PDF

  43. R. Song and Z. Vondracek: Sharp bounds for Green functions and jumping functions subordinate killed Brownian motions in bounded $C^{1, 1}$ domains. Electron. Comm. Probab., Vol. 9 (2004), 96--105. PDF

  44. R. Song and Z. Vondracek: Harnack inequality for some discontinuous Markov processes with a diffusion part. Glas. Mat., Vol. 40, No. 1 (2005), 177--187. Postscript PDF

  45. Z. Chen and R. Song: Two-sided Eigenvalue Estimates for Subordinate Processes in Domains. J. Funct. Anal., Vol. 226, No. 1 (2005), 90--113. PDF

  46. M. Rao, R. Song and Z. Vondracek: Green function estimates and Harnack inequality for subordinate Brownian motions. Potential Anal., Vol. 25, No. 1 (2006), 1--27. PDF

  47. Z. Chen and R. Song: Continuity of eigenvalues for Subordinate Processes in Domains. Math. Z., Vol. 252, No. 1 (2006), 71--89. PDF

  48. R. Song: Estimates on the transition density of Girsanov transforms of symmetric stable processes, J. Theoret. Probab., Vol. 19, No. 2 (2006), 487--507 PDF

  49. R. Song and Z. Vondracek: Potential theory of special subordinators and subordinate killed stable processes. J. Theoret. Probab., Vol. 19, No. 4 (2006), 817--847. PDF

  50. H. Sikic, R. Song and Z. Vondracek: Potential theory of geometric stable processes. Probab. Theory Related Fields, Vol. 135, No. 4 (2006), 547--575. PDF

  51. R. Song: Two-sided estimates on the density of the Feynman-Kac semigroups of stable-like processes. Electron. J. Probab., Vol. 11, No. 6 (2006), 146--161 PDF

  52. R. Song and Z. Vondracek: On the monotonicity of a function related to the local time of a symmetric Levy process. Statist. Probab. Lett., Vol. 76, No. 14 (2006), 1522--1528. PDF

  53. P. Kim and R. Song: Two-sided estimates on the density of Brownian motion with singualr drift Illinois J. Math., Vol. 50 (2006), 635--688 PDF

  54. R. Song and Z. Vondracek: Parabolic Harnack Inequality for the Mixture of Brownian Motion and Stable Process. Tohoku Math. J., Vol. 59, No. 1 (2007), 1--19. PDF

  55. P. Kim and R. Song: Potential Theory of truncated stable processes. Math. Z., Vol. 256, No. 1 (2007), 139--173. PDF

  56. Z.-Q. Chen and R. Song: Spectral properties of subordinate processes in domains. Stochastic Analysis and Partial Differential Equations (edited by G.-Q. Chen, E. P. Hsu and M. Pinsky), 77-84, AMS, 2007. PDF

  57. P. Kim and R. Song: Estimates on Green functions and Schrodinger-type equations for non-symmetric diffusions with measure-valued drifts. J. Math. Anal. Appl., Vol. 332, No. 1 (2007), 57--80. PDF

  58. P. Kim and R. Song: Boundary Harnack principle for Brownian motions with measure-valued drifts in bounded Lipschitz domains. Math. Ann., Vol. 339, No. 1 (2007), 135--174. PDF

  59. P. Kim and R. Song: On dual processes of non-symmetric diffusions with measure-valued drifts. Stoch. Proc. Appl., Vol. 118 (2008), 790--817. PDF

  60. P. Kim and R. Song: Boundary behavior of harmonic functions for truncated stable processes. J. Theoret. Probab., Vol. 21 (2008), 287--321. PDF

  61. P. Kim and R. Song: Intrinsic ultracontractivity of non-symmetric diffusions with measure-valued drifts and potentials. Ann. Probab., Vol. 36 (2008), 1904--1945. PDF

  62. R. Song and Z. Vondracek: On suprema of Levy processes and application in risk theory. Ann. Inst. H. Poincare, Probab. Statist., Vol. 44 (2008), 977--986. PDF

  63. P. Kim and R. Song: Intrinsic ultracontractivity of non-symmetric diffusion semigroups in bounded domains. Tohoku Math. J., Vol. 60 (2008), 527--547. PDF

  64. R. Song and Z. Vondracek: On the Relationship between subordinate killed and killed subordinate processes Elect. Commun. Probab.,Vol. 13 (2008), 325--336 PDF

  65. P. Kim and R. Song: Intrinsic ultracontractivity for non-symmetric Levy processes. Forum Math., Vol. 21 (2009), 43--66. PDF

  66. Y.-X. Ren, R. Song and H. Wang: A class of stochastic partial differential equations for interacting superprocesses on a bounded domain. Osaka J. Math., Vol. 46(2009), 373--401 PDF

  67. P. Kim, R. Song and Z. Vondracek: Boundary Harnack Principle for Subordinate Brownian Motions. Stoch. Proc. Appl., Vol. 119 (2009), 1601--1631. PDF

  68. R.-L. Liu, Y.-X. Ren and R. Song: LlogL criterion for a class of super-diffusions. J. Appl. Probab., Vol. 46 (2009), 479--496 PDF

  69. R. Song and Z. Vondracek: Potential theory of subordinate Brownian motion. In "Lecture Notes in Math., Vol. 1980", 2009. PDF

  70. Z.-Q. Chen, P. Kim and R. Song: Heat kernel estimates for Dirichlet fractional Laplacian. J. European Math. Soc., Vol. 12 (2010), 1307--1329. PDF

  71. R. Song and Z. Vondracek: Some remarks on special subordinators. Rocky Mountain J. of Math., Vol. 40 (2010), 321--337. PDF

  72. Z.-Q. Chen, P. Kim and R. Song: Two-sided heat kernel estimates for censored stable-like processes. Probab. Theory Relat. Fields, Vol. 146 (2010), 361--399. PDF

  73. A. Kyprianou, V. Rivero and R. Song: Convexity and smoothness of scale functions and de Finetti's control problem J. Theoret. Probab., Vol. 23 (2010), 547--564. PDF

  74. P. Kim, R. Song and Z. Vondracek: On the potential theory of one-dimensional subordinate Brownian motions with continuous components. Potential Analysis, Vol. 33 (2010), 153--173 PDF

  75. Z.-Q. Chen, P. Kim, R. Song and Z. Vondracek: Sharp Green function estimates for $\Delta + \Delta^{\alpha/2}$ in $C^{1, 1}$ open sets and their applications. Illinois J. Math. Vol. 54 (2010), 981--1024. PDF

  76. Z.-Q.. Chen, P. Kim and R. Song Dirichlet heat kernel estimates for $\Delta^{\alpha/2} +\Delta^{\beta/2}$. Illinois J. Math. Vol. 54 (2010), 1357--1392. PDF

  77. R.-L. Liu, Y.-X. Ren and R. Song: LlogL condition for supercritical branching Hunt processes. J. Theoretical Probab., Vol. 24 (2011), 170--193 PDF

  78. Z.-Q.. Chen, P. Kim and R. Song: Green function estimates for relativistic stable processes in half-space like open sets. Stochastic Process. Appl., Vol. 121 (2011), 1148--1172 PDF

  79. Z.-Q.. Chen, P. Kim and R. Song: Heat kernel estimates for $\Delta + \Delta^{\alpha/2}$ in $C^{1, 1}$ open sets. J. London Math. Soc., Vol. 84 (2011), 58--80 PDF

  80. P. Kim, R. Song and Z. Vondracek: On harmonic functions for trace processes. Math. Nach., Vol. 284 (2011), 1889--1902. PDF

  81. A. Chen, L. Feng and R. Song: On the monitoring error of the supremum of a normal jump diffusion process. J. Appl. Probab., Vol. 48 (2011), 1021--1034 PDF

  82. Z.-Q.. Chen, P. Kim, R. Song and Z. Vondracek: Boundary Harnack principle for $\Delta + \Delta^{\alpha/2}$. Trans. Amer. Math. Soc. Vol. 364 (2012), 4169--4205 PDF

  83. Z.-Q.. Chen, P. Kim and R. Song Sharp heat kernel estimates for relativistic stable processes in open sets. Ann. Probab. Vol. 40 (2012), 213--244 PDF

  84. Z.-Q.. Chen, P. Kim and R. Song: Global heat kernel estimates for relativistic stable processes in half-space-like open sets. Potential Analysis. Vol. 36 (2012), 235--261 PDF

  85. Z.-Q.. Chen, P. Kim and R. Song: Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation. Ann. Probab. Vol. 40 (2012), 2483--2538 PDF

  86. P. Kim, R. Song and Z. Vondracek: Potential theory of subordinate Brownian motions revisited. Stochastic Analysis and Applications to Finance--Essays in Honour of Jia-an Yan, edited by Tusheng Zhang & Xunyu Zhou. World Scientific, 2012, pages 243--290. PDF

  87. P. Kim, R. Song and Z. Vondracek: Minimal thinness for subordinate Brownian motion in half space. Annales de l'Institut Fourier, Vol. 62 (2012), 1045--1080 PDF

  88. P. Kim, R. Song and Z. Vondracek: Two-sided Green function estimates for killed subordinate Brownian motions. Proc. London Math. Soc. Vol. 104(2012), 927--958 PDF

  89. L. Bo, R. Song, D. Tang, Y. Wang and X. Yang: Levy risk model with two-sided jumps and a barrier dividend strategy. Insurance: Mathematics and Economics, Vol. 50(2012), 280--291 PDF

  90. Z.-Q. Chen, P. Kim and R. Song: Global Heat Kernel Estimates for $\Delta+\Delta^{\alpha/2}$ in Half-space-like domains. Elect. J. Probab. Vol. 17 (2012), No. 32, 1--32 PDF

  91. Z.-Q. Chen, P. Kim and R. Song: Global Heat Kernel Estimates for Relativistic Stable Processes in Exterior Open Sets. J. Funct. Anal. Vol. 263 (2012), 448--475. PDF

  92. P. Kim, R. Song and Z. Vondraecek: Uniform boundary Harnack principle for rotationally symmetric Levy processes in general open sets. Science China Mathematics Vol. 55, (2012), 2317--2333 PDF

  93. R.-L. Liu, Y.-X. Ren and R. Song Strong law of large numbers for a class of superprocesses. Acta. Appl. Math. Vol. 123 (2013), 73--97 PDF

  94. P. Kim, H. Park and R. Song: Sharp estimates on the Green functions of perturbations of subordinate Brownian motions in bounded $\kappa$-fat open sets. Potential Analysis, Vol. 38 (2013), 319--344 PDF

  95. P. Kim, R. Song and Z. Vondracek: Potential theory of subordinate Brownian motions with Gaussian components. Stoch. Proc. Appl. Vol. 123 (2013), 764--795. PDF

  96. P. Kim, R. Song and Z. Vondracek: Global uniform boundary Hanack principle with explicit decay rate and its application. Stoch. Proc. Appl. Vol. 124 (2014), 235-267. PDF

  97. Y.-X. Ren, R. Song and R. Zhang: Central limit theorem for super Ornstein-Uhlenbeck proceses. Acta Appl. Math. Vol. 130 (2014), 9--49. PDF

  98. Z.-Q. Chen, P. Kim and R. Song: Dirichlet heat kernel estimates for rotationally symmetric Levy processes. Proc. London Math. Soc. Vol. 109 (2014), 90--120 PDF

  99. J. Zhang, S. Li and R. Song: Quasi-stationarity and quasi-ergodicity of general Markov processes. Science China Math. Vol. 57 (2014), 2013--2024 PDF

  100. P. Kim, R. Song and Z. Vondracek: Boundary Harnack principle and Martin boundary at infinity for subordinate Brownian motions. Potential Analysis, Vol. 41 (2014), 407--441 PDF

  101. P. Kim and R. Song: Stable process with singular drift. Stoch. Proc. Appl. Vol. 124 (2014) 2479--2516. PDF

  102. P. Kim and R. Song: Dirichlet heat kernel estimates for stable processes with singular drift in unbounded C^{1,1} open sets. Potential Analysis, Vol. 41 (2014), 555--581 PDF

  103. Y.-X. Ren, R. Song and R. Zhang: Central Limit Theorems for Supecritical Branching Markov Processes. Journal of Functional Analysis, Vol. 266 (2014), 1716--1756. PDF

  104. T. Gao, J. Duan, X. Li and R. Song: Mean Exit Time and Escape Probability for Dynamical Systems Driven by Levy Noises. SIAM J. Scientific Computing. Vol. 36 (2014), A887--A906. PDF

  105. H. Meng, J. Duan, R. Song and W. Xu: Asymmetric non-Gaussian effects in a tumor growth model with immunization. Appl. Math. Model. Vol. 38 (2014), 4428--4444. PDF

  106. P. Kim, R. Song and Z. Vondracek: Martin boundary for some symmetric Levy processes. Festschrift Masatoshi Fukushima, pp. 307--342. PDF

  107. H. Park and R. Song Trace estimates for relativistic stable processes. Potential Analysis, Vol. 41 (2014), 1273--1291. PDF

  108. Z.-Q. Chen, P. Kim and R. Song: Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation. Trans. Amer. Math. Soc. Vol. 367 (2015), 5237--5270. PDF

  109. Y.-X. Ren, R. Song and R. Zhang: Central Limit Theorems for Supecritical Superrocesses. Stoch. Proc. Appl. Vol. 125 (2015), 428--457 PDF

  110. Z.-Q. Chen, Y.-X. Ren, R. Song and R. Zhang: Strong law of large numbers for supercritical superprocesses under second momemnt condition. Front. Math. China. Vol. 10(4) (2015), 807--838. PDF

  111. Y.-X. Ren, R. Song and R. Zhang: Limit theorems for some critical superprocesses. Illinois J. Math. Vol. 59 (2015), 235--276. PDF

  112. Z.-Q. Chen, P. Kim and R. Song: Dirichlet heat kernel estimates for subordinate Brownian motions with Gaussian components. Journal fur reine und angewandte Mathematik Vol. 711 (2016), 111--138 PDF

  113. J. Englander, Y.-X. Ren and R. Song: Weak extinction versus global exponential growth of total mass for superdiffusions. Ann. l'Institut Henri Poincare, Vol. 52 (2016), 448--482. PDF

  114. P. Kim, R. Song and Z. Vondracek: Minimal thinness with respect to symmetric Levy processes. Trans. Amer. Math. Soc. Vol. 368 (2016), 8785--8822 PDF

  115. P. Kim, R. Song and Z. Vondracek: Minimal thinness with respect to subordinate killed Brownian motions. Stoch Proc Appl. Vol. 126 (2016), 1226--1263 PDF

  116. P. Kim, R. Song and Z. Vondracek: Martin boundary of unbounded sets for purely discontinuous Feller processes. Forum Math. Vol. 28 (2016), 1067--1085. PDF

  117. Y.-X. Ren, R. Song and R. Zhang: Central limit theorems for supercritical branching nonsymmetric Markov processes. Ann. Probab. Vol. 45 (2017), 564--623 PDF

  118. Y.-X. Ren, R. Song and R. Zhang: Functional central limit theorems for supercritical superprocesses. Acta Appl. Math. Vol. 147 (2017), 137--175. PDF

  119. P. Kim, R. Song and Z. Vondracek: Scale invariant boundary Harnack principle at infinity for Feller processes. Pot. Anal. Vol. 47 (2017), 337--367. PDF

  120. P. Kim, R. Song and Z. Vondracek: Accessibility, Martin boundary and minimal thinness for Feller processes in metric measure spaces. To appear in Rev. Mat. Iberoam. PDF

  121. Z.-Q. Chen, R. Song and X. Zhang: Stochastic flows for Levy processes with Holder drifts. To appear in Rev. Mat. Iberoam. PDF

  122. P. Kim, R. Song and Z. Vondracek: Heat kernels of non-symmetric jump processes: beyond the stable case. To appear in Pot. Anal. PDF

  123. P. Kim, R. Song and Z. Vondracek: Potential theory of subordinate killed Brownian motions. To appear in Trans. Amer. Math. Soc. PDF

  124. Y.-X. Ren, R. Song and R. Zhang: Williams decomposition for superprocesses Elect J Probab. Vol 23 (2018), no. 23, 1--33.PDF

  125. L. Feng, S. Li, R. Song and Y. Li: Explosion suppression by polynomial noise for nonlinear differential systems. To appear in Sci China Info Sci PDF

  126. Z.-Q. Chen, Y.-X. Ren and R. Song: $L\log L$ criterion for a class of multitype superdiffusions with non-local branching mechanisms. To appear in Sci. China Math. PDF