PUBLICATIONS


  1. Stochastic analysis on the extended sample space and tightness results.
    Probab. Theory Relat. Fields, 86 (1990), 517-549.

  2. On reflected Dirichlet spaces.
    Probab. Theory Relat. Fields, 94 (1992), 135-162.

  3. Pseudo Jordan domains and reflecting Brownian motions.
    Probab. Theory Relat. Fields, 94 (1992), 271-280.

  4. On reflecting diffusion processes and Skorokhod decompositions.
    Probab. Theory Relat. Fields, 94 (1993), 281-316.

  5. Reflecting Brownian motions: quasimartingales and strong Caccioppoli sets.
    Potential Analysis, 2 (1993), 219-243. (with P.J. Fitzsimmons and R.J. Williams)

  6. The binding capacity is a probability density function.
    Biophysical Journal, 65 (1993), 164-170. (with E. DiCera)

  7. Switched diffusion processes and systems of elliptic equations--a Dirichlet space approach.
    Proc. Royal Soc. Edinburgh, 124A (1994), 673-701. (with Z. Zhao)

  8. On the existence of positive solutions of semilinear elliptic equations with Dirichlet boundary conditions.
    Math. Ann. 298 (1994), 543-556. (with R.J. Williams and Z. Zhao)

  9. A Sobolev inequality and Neumann heat kernel estimate for unbounded domains.
    Math. Research Letters, 1 (1994), 177-184. (with R.J. Williams and Z. Zhao)

  10. Quasi-homeomorphisms of Dirichlet forms.
    Nagoya J. Math. 136 (1994), 1-15. (with Z.M. Ma and M. Roeckner)

  11. Diffusion processes and second order elliptic operators with singular coefficients for lower order terms.
    Math. Ann. 302 (1995), 323-357. (with Z. Zhao)

  12. On the existence of positive solutions of semilinear elliptic equations with Neumann boundary conditions.
    Probab. Theory Relat. Fields, 101 (1995), 251-276. (with R.J. Williams and Z. Zhao)

  13. Non-negative solutions for semilinear elliptic equations with boundary conditions--a probabilistic approach.
    Proceedings of Symposia in Pure Mathematics, vol. 57 (1995), 65-82. (with R.J. Williams and Z. Zhao)

  14. Reflecting Brownian motions and a deletion result for Sobolev spaces of order (1,2).
    Potential Analysis, 5 (1996). 383-401.

  15. Potential theory for elliptic systems.
    Ann. Probab. 24 (1996), 293-319. (with Z. Zhao)

  16. Holomorphic diffusions and boundary behavior of harmonic functions.
    Ann. Probab. 25 (1997), 1103-1134. (with R. Durrett and G. Ma)

  17. Harnack principle for weakly coupled elliptic systems.
    Journal of Differential Equations, 139 (1997), 261-282. (with Z. Zhao)

  18. Stability and approximations of symmetric diffusion semigroups and kernels.
    J. Funct. Anal. 152 (1998), 255-280. (with Y. Hu, Z. Qian and W. Zheng)

  19. Estimates on Green functions and Poisson kernels of symmetric stable processes in bounded domains.
    Math. Ann. 312 (1998), 465-501. (with R. Song)

  20. Intrinsic ultracontractivity and conditional gauge for symmetric stable processes.
    J. Funct. Anal. 150 (1997), 204-239. (with R. Song)

  21. Weak convergence of reflecting Brownian motions.
    Elect. Comm. Probab. 3 (1998), 29-33. (with K. Burdzy)

  22. Martin boundary and integral representation for harmonic functions of symmetric stable processes.
    J. Funct. Anal. 159 (1998), 267-294. (with R. Song)

  23. On the existence of positive solutions for semilinear elliptic equations with singular lower order coefficients and Dirichlet boundary conditions.
    Math. Ann. 315 (1999), 735--769. (with R.J. Williams and Z. Zhao)

  24. Intrinsic ultracontractivity, conditional lifetimes and conditional gauge for symmetric stable processes on rough domains.
    Ill. J. Math. 44 (2000), 138--160. (with R. Song)

  25. Local time flow related to skew Brownian motion.
    Ann. Probab. 29 (2001), 1693--1715. (with K. Burdzy)

  26. Multidimensional symmetric stable processes.
    Korean J. Comput. Appl. Math. 6 (1999), 227-266

  27. Crossing estimates for symmetric Markov processes.
    Probab. Theory Relat. Fields. 120 (2001), 68-84. (with P.J. Fitzsimmons and R. Song)

  28. A Note on Green function estimates for symmetric stable processes.
    In Recent Developments in Stochastic Analysis and Related Topics, p.125-135.
    Proceedings of the First Sino-German Conference on Stochastic Analysis (2002). World Scientific, 2004. (with R. Song)

  29. Stochastic differential equations for Dirichlet processes.
    Probab. Theory Relat. Fields, 121 (2001), 422-446. (with R. Bass)

  30. The heat equation in time dependent domains with insulated boundaries.
    J. Math. Anal. Appl. 294 (2004), 581-595. (with K. Burdzy and J. Sylvester)

  31. Heat equation and reflected Brownian motion in time dependent domains.
    Ann. Probab. 32 (2004), 775-804. (Joint with K. Burdzy and J. Sylvester)

  32. Heat equation and reflected Brownian motion in time dependent domains II: Singularities of Solutions.
    J. Funct. Anal. 204 (2003), 1-34. (with K. Burdzy and J. Sylvester)

  33. Girsanov and Feynman-Kac type transformations for symmetric Markov processes.
    Ann. Inst. Henri Poincare Probab. Statist., 38 (2002), 475-505. (with T.-S. Zhang)

  34. General gauge and conditional gauge theorems.
    Ann. Probab. 30 (2002), 1313-1339. (with R. Song)

  35. Brownian motion with singular drift.
    Ann. Probab. 31 (2003), 791-817. (with R. Bass)

  36. Coalescence of synchronous couplings.
    Probab. Theory Relat. Fields, 123 (2002), 553--578. (with K. Burdzy)

  37. Conditional gauge theorem for non-local Feynman-Kac transforms.
    Probab. Theory Relat. Fields, 125 (2003), 45-72. (with R. Song)

  38. Gaugeability and conditional gaugeability.
    Trans. Amer. Math. Soc. 354 (2002), 4639--4679.

  39. Censored stable processes.
    Probab. Theory Relat. Fields. 127 (2003), 89--152. (with K. Bogdan and K. Burdzy)

  40. Hardy inequality for censored stable processes.
    Tohoku Math. J. 55 (2003), 439-450. (with R. Song)

  41. Drift transforms and Green function estimates for discontinuous processes.
    J. Funct. Anal. 201 (2003), 262-281. (with R. Song)

  42. Green function estimate for censored stable processes.
    Probab. Theory Relat. Fields 124 (2002), 595-610. (with P. Kim)

  43. Uniqueness for reflecting Brownian motion in lip domains.
    Ann. Inst. Henri Poincare Probab. Statist. 41 (2005), 197-235. (with R. Bass and K. Burdzy)

  44. Analytic characterization of conditional gaugeability for non-local Feynman-Kac transforms.
    J. Funct. Anal. 202 (2003), 226-246.

  45. Absolute continuity of symmetric Markov processes.
    Ann. Probab. 32 (2004), 2067-2098. (Joint with P.J. Fitzsimmons, M. Takeda, J. Ying and T.-S. Zhang)

  46. Stochastic differential equations driven by stable processes for which pathwise uniqueness fails.
    Stochastic Process Appl. 111 (2004), 1-15. (with R. Bass and K. Burdzy)

  47. Heat kernel estimates for stable-like processes on d-sets.
    Stochastic Process Appl. 108 (2003), 27-62. (with T. Kumagai)

  48. Traps for reflecting Brownian motion.
    Math. Z. 252 (2006), 103-132. (with K. Burdzy and D. Marshall)

  49. Stability of Martin boundary under non-local Feynman-Kac perturbations.
    Probab. Theory Relat. Fields, 128 (2004), 525-564. (with P. Kim)

  50. Boundary trace of reflecting Brownian motions.
    Probab. Theory Relat. Fields, 129 (2004), 1-17. (with I. Benjamini and S. Rohde)

  51. Systems of equations driven by stable processes.
    Probab. Theory Relat. Fields, 134 (2006), 175-214. (with R. Bass)

  52. One-dimensional stochastic differential equations with singular and degenerate coefficients.
    Sankhya 67 (2005), 19-45. (with R. Bass)

  53. Two-sided eigenvalue estimates for subordinate processes in domains.
    J. Funct. Anal. 226 (2005), 90-113. (with R. Song)

  54. Traces of symmetric Markov processes and their characterizations
    Ann. Probab. 34 (2006), 1052-1102. (with M. Fukushima and J. Ying)

  55. Continuity of eigenvalues of subordinate processes in domains.
    Math. Z. 252 (2006), 71-89. (with R. Song)

  56. Synchronous couplings of reflected Brownian motions in smooth domains.
    Ill. J. Math. 50 (2006) (Special volume in memory of Joseph Doob), 189-268. (with K. Burdzy and P. Jones)

  57. Entrance law, exit system and Levy system of time-changed processes.
    Ill. J. Math. 50 (2006) (Special volume in memory of Joseph Doob), 269-312. (with M. Fukushima and J. Ying)

  58. On the Robin problem in fractal domains.
    Proc. London Math. Soc. 96 (2008), 273-311. (with R. F. Bass and K. Burdzy)

  59. Comparision of potential theoretic properties of rough domains.
    Proc. Amer. Math. Soc. 134 (2006), 3247-3253. (with K. Burdzy)

  60. Shy couplings.
    Probab. Theory Relat. Fields, 137 (2007), 345-377. (with I. Benjamini and K. Burdzy)

  61. Spectral properties of subordinate processes in domains.
    In Stochastic Analysis and Partial Differential Equations, 77-84.
    (Eds. G-Q Chen, E. Hsu and M. Pinsky.) AMS Compt. Math. 429 (2007). (with R. Song)

  62. Extending Markov processes in weak duality by Poisson point processes of excursions.
    Proceedings of the Abel Symposium 2005, Stochastic Analysis and Applications-A Symposium in Honor of Kiyosi Ito.
    (Eds. F.E. Benth, G. Di Nunno, T. Lindstrom, B. Oksendal and T. Zhang.) Springer, 2007, pp153-196. (with M. Fukushima and J. Ying)

  63. Pathwise uniqueness for a degenerate stochastic differential equation.
    Ann. Probab. 35 (2007), 2385-2418. (with R. Bass and K. Burdzy)

  64. Heat kernel estimates for jump processes of mixed types on metric measure spaces.
    Probab. Theory Relat. Fields 140 (2008), 277-317. (with T. Kumagai)

  65. One-point extensions of Markov processes by darning.
    Probab. Theory Relat. Fields 141 (2008), 61-112. (with M. Fukushima)

  66. Stochastic calculus for symmetric Markov processes.
    Ann. Probab. 36 (2008), 931-970. Errata. Ann. Probab. 40 (2012), 1375-1376. (with P. J. Fitzsimmons, K. Kuwae and T.-S. Zhang)

  67. Perturbation of symmetric Markov processes.
    Probab. Theory Relat. Fields 140 (2008), 239-275. (with P. J. Fitzsimmons, K. Kuwae and T.-S. Zhang)

  68. Non-local Dirichlet forms and symmetric jump processes.
    Trans. Amer. Math. Soc. 361 (2009), 1963-1999. (with M. T. Barlow, R. F. Bass and M. Kassmann)

  69. Limit theorems for branching Markov processes.
    J. Funct. Anal. 250 (2007), 374-399. (with Y. Shiozawa)

  70. On Feller's boundary problem for Markov processes in weak duality.
    J. Funct. Anal. 252 (2007), 710-733. (with M. Fukushima)

  71. Discrete approximations to reflected Brownian motion.
    Ann. Probab. 36 (2008), 698-727. (with K. Burdzy)

  72. On Feynman-Kac perturbation of symmetric Markov processes.
    In Proceedings of Functional Analysis IX, Dubrovnik, Croatia, 2005, pp. 39-43.

  73. Interacting superprocesses with discontinuous spatial motion.
    Forum Math. 24 (2012), 1183-1223. (with H. Wang and J. Xiong)

  74. Flux and lateral conditions for symmetric Markov processes.
    Potential Analysis 29 (2008), 241-269. (with M. Fukushima)

  75. Schramm-Loewner equations driven by symmetric stable processes.
    Comm. Math. Phys. 285 (2009), 799-824. (with S. Rohde)

  76. An almost sure scaling limit theorem for Dawson-Watanabe superprocesses
    J. Funct. Anal. 254 (2008), 1988-2019. (with Y. Ren and H. Wang)

  77. Exit time, Green function and semilinear elliptic equations.
    Elect. J. Probab. 14 (2009), 50-71. (with R. Atar and S. Athreya)

  78. Weighted Poincaré inequality and heat kernel estimates for finite range jump processes.
    Math. Ann. 342 (2008), 833-883. (with P. Kim and T. Kumagai)

  79. Time-reversal and elliptic boundary value problems.
    Ann. Probab. 37 (2009), 1008-1043. (with T.-S. Zhang)

  80. On general perturbations of symmetric Markov processes.
    J. Math. Pures et Appliquées 92 (2009), 363-374. (with P. Fitzsimmons, K. Kuwae and T.-S. Zhang)

  81. Stochastic evolution equations driven by stable processes.
    Osaka J. Math. 48 (2011), 311-327. (with T.-S. Zhang)

  82. Heat kernel estimates for Dirichlet fractional Laplacian.
    J. Euro. Math. Soc. 12 (2010), 1307-1329. (with P. Kim and R. Song)

  83. Two-sided heat kernel estimates for censored stable-like processes.
    Probab. Theory Relat. Fields 146 (2010), 361-399. (with P. Kim and R. Song)

  84. Stationary distributions for diffusions with inert drift.
    Probab. Theory Relat. Fields 146 (2010), 1-47. (with R. Bass, K. Burdzy and M. Hairer)

  85. On doubly Feller property.
    Osaka J. Math. 46 (2009), 909-930. (with K. Kuwae)

  86. On unique extension of time changed reflecting Brownian motions.
    Ann. Inst. Henri Poincare Probab. Statist. 45 (2009), 864-875. (with M. Fukushima)

  87. A priori Hölder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps.
    Revista Matematica Iberoamericana 26 (2010), 551-589. (with T. Kumagai)

  88. On notions of harmonicity.
    Proc. Amer. Math. Soc. 137 (2009), 3497-3510.

  89. On heat kernel estimates and parabolic Harnack inequality for jump processes on metric measure spaces.
    Acta Mathematica Sinica, English Series 25 (2009), 1067-1086. (with P. Kim and T. Kumagai)

  90. Symmetric jump processes and their heat kernel estimates.
    Sci. China Ser. A. 52 (2009), 1423-1445.

  91. Boundary Harnack principle for Δ + Δα/2.
    Trans. Amer. Math. Soc. 384 (2012), 4169-4205. (with P. Kim, R. Song and Z. Vondracek)

  92. Regularity of harmonic functions for a class of singular stable-like processes.
    Math. Z. 266 (2010), 489-503. (with R. F. Bass)

  93. Global heat kernel estimates for fractional Laplacians in unbounded open sets.
    Probab. Theory Relat. Fields. 149 (2011), 373-395. (with J. Tokle)

  94. Sharp heat kernel estimates for relativistic stable processes in open sets.
    Ann. Probab. 40 (2012), 213-244. (with P. Kim and R. Song)

  95. Green function estimates for relativistic stable processes in half-space-like open sets.
    Stochastic Process Appl. 121 (2011), 1148-1172. (with P. Kim and R. Song)

  96. Dirichlet heat kernel estimates for Δα/2 + Δβ/2.
    Ill. J. Math. 54 (2010) (Special issue in honor of D. Burkholder), 1357-1392. (with P. Kim and R. Song)

  97. An L2-theory for a class of SPDEs driven by Lévy processes.
    Sci. in China, Series A 55 (2012) (Special issue on Probability), 2233-2246. (with K.-H. Kim)

  98. Sharp Green function estimates for Δ + Δα/2 in C1,1 open sets and their applications.
    Ill. J. Math. 54 (2010) (Special issue in honor of D. Burkholder), 981-1024. (with P. Kim, R. Song and Z. Vondracek)

  99. On subhamonicity for symmetric Markov processes.
    J. Math. Soc. Japan, 64 (2012), 1181-1209. (with K. Kuwae)

  100. Archimedes' principle for Brownian liquid.
    Ann. Appl. Probab. 21 (2011), 2053-2074. (with K. Burdzy and S. Pal)

  101. Heat kernel estimates for Δ + Δα/2 in C1,1 open sets.
    J. London Math. Soc. 84 (2011), 58-80. (with P. Kim and R. Song)

  102. Global heat kernel estimates for symmetric jump processes.
    Trans. Amer. Math. Soc. 363 (2011), 5021-5055. (with P. Kim and T. Kumagai)

  103. An Lp-theory of non-divergence form SPDEs driven by Lévy processes.
    To appear in Forum Math. (with K.-H. Kim)

  104. Discrete approximation of symmetric jump processes on metric measure spaces.
    Probab. Theory Relat. Fields 155 (2013), 703-749. (with P. Kim and T. Kumagai)

  105. Global heat kernel estimate for relativistic stable processes in half-space-like open sets.
    Potential Analysis. 36 (2012), 235-261. (with P. Kim and R. Song)

  106. Dirichlet heat kernel estimates for fractional Laplacian under gradient perturbation.
    Ann. Probab. 40 (2012), 2483-2538. (with P. Kim and R. Song)

  107. Brownian earthworm.
    To appear in Ann. Probab. (with K. Burdzy and S. Pal)

  108. A localization formula in Dirichlet form theory.
    Proc. Amer. Math. Soc. 140 (2012), 1815-1822. (with M. Fukushima)

  109. Global heat kernel estimates for Δ + Δα/2 in half-space-like domains.
    Eletronic J. Probab.17 (2012), Paper 32, 1-31. (with P. Kim and R. Song)

  110. Uniform integrability of exponential martingales and spectral bounds of non-local Feynman-Kac semigroups.
    In Stochastic Analysis and Applications to Finance, Essays in Honor of Jia-an Yan. (Eds by T. Zhang and X. Zhou), 2012. pp.55-75.

  111. Reflecting random walk in fractal domains.
    To appear in Ann. Probab. (with K. Burdzy)

  112. Lp-independence of spectral bounds of generalized non-local Feynman-Kac semigroups
    J. Funct. Anal. 262 (2012), 4120-4139.

  113. Space-time fractional diffusion on bounded domains.
    J. Math. Anal. Appl. 393 (2012), 479-488. (with M. M. Meerschaert and E. Nane)

  114. Global heat kernel estimate for relativistic stable processes in exterior open sets.
    J. Funct. Anal. 263 (2012), 448-475. (with P. Kim and R. Song)

  115. Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation.
    To appear in Trans. Amer. Math. Soc. (with P. Kim and R. Song)

  116. A probabilistic approach to mixed boundary value problems for elliptic operators with singular coefficients.
    To appear in Proc. Amer. Math. Soc. (with T. Zhang)

  117. Perturbation by non-local operators.
    Preprint 2012. (with J. Wang)

  118. Chordal Komatu-Loewner equation and Brownian motion with darning in multiply connected domains.
    Preprint 2013. (with M. Fukushima and S. Rohde)

  119. Dirichlet heat kernel estimates for rotationally symmetric L\'evy processes.
    Preprint 2013. (with P. Kim and R. Song)

  120. Dirichlet heat kernel estimates for subordinate Brownian motions with Gaussian components.
    To appear in J. Reine Angew. Math.. (with P. Kim and R. Song)

  121. Uniqueness of stable processes with drifts.
    Preprint 2013. (with L. Wang)

  122. Quenched invariance principles for random walks and elliptic diffusions in random media with boundary.
    Preprint 2013. (with D.A. Croydon and T. Kumagai)

  123. On uniform positivity of transition densities of small noise constrained diffusions.
    Preprint 2013. (with A. Budhiraja)

  124. Heat kernels and analyticity of non-symmetric jump diffusion semigroups.
    Preprint 2013. (with X. Zhang)