PUBLICATIONS
 Stochastic analysis on the extended sample space and tightness
results.
Probab. Theory Relat. Fields, 86 (1990),
517549.
 On reflected Dirichlet spaces.
Probab. Theory
Relat. Fields, 94 (1992), 135162.
 Pseudo Jordan domains and reflecting Brownian motions.
Probab. Theory Relat. Fields, 94 (1992), 271280.
 On reflecting diffusion processes and Skorokhod
decompositions.
Probab. Theory Relat. Fields, 94 (1993), 281316.
 Reflecting
Brownian motions: quasimartingales and strong Caccioppoli sets.
Potential Analysis, 2 (1993), 219243.
(with P.J. Fitzsimmons and R.J. Williams)
 The binding capacity is a probability
density function.
Biophysical Journal, 65 (1993), 164170.
(with E. DiCera)
 Switched diffusion processes and systems
of elliptic equationsa Dirichlet space approach.
Proc. Royal Soc. Edinburgh, 124A (1994),
673701. (with Z. Zhao)
 On the existence of
positive solutions of semilinear elliptic equations with Dirichlet
boundary conditions.
Math. Ann. 298 (1994),
543556. (with R.J. Williams and Z. Zhao)
 A Sobolev inequality
and Neumann heat kernel estimate for unbounded domains.
Math. Research Letters, 1 (1994), 177184.
(with R.J. Williams and Z. Zhao)
 Quasihomeomorphisms of
Dirichlet forms.
Nagoya J. Math. 136 (1994), 115.
(with Z.M. Ma and M. Roeckner)
 Diffusion processes and second order
elliptic operators with singular coefficients for lower order terms.
Math. Ann. 302 (1995), 323357.
(with Z. Zhao)
 On the existence of
positive solutions of semilinear elliptic equations with Neumann
boundary conditions.
Probab. Theory Relat.
Fields, 101 (1995), 251276.
(with R.J. Williams and Z. Zhao)
 Nonnegative
solutions for semilinear elliptic equations with
boundary conditionsa probabilistic approach.
Proceedings of Symposia in Pure Mathematics,
vol. 57 (1995), 6582.
(with R.J. Williams and Z. Zhao)
 Reflecting Brownian motions
and a deletion result for Sobolev spaces of order (1,2).
Potential Analysis, 5 (1996). 383401.
 Potential theory for elliptic systems.
Ann. Probab. 24 (1996), 293319.
(with Z. Zhao)
 Holomorphic diffusions and
boundary behavior of harmonic functions.
Ann. Probab. 25 (1997), 11031134.
(with R. Durrett and G. Ma)
 Harnack principle for weakly coupled elliptic systems.
Journal of Differential Equations, 139 (1997), 261282.
(with Z. Zhao)
 Stability and approximations
of symmetric diffusion semigroups and kernels.
J. Funct. Anal. 152 (1998), 255280.
(with Y. Hu, Z. Qian and W. Zheng)
 Estimates on Green functions and Poisson kernels
of symmetric stable processes in bounded domains.
Math. Ann. 312 (1998), 465501.
(with R. Song)
 Intrinsic ultracontractivity and conditional
gauge for symmetric stable processes.
J. Funct. Anal. 150 (1997), 204239.
(with R. Song)
 Weak convergence of reflecting Brownian motions.
Elect. Comm. Probab. 3 (1998), 2933.
(with K. Burdzy)
 Martin boundary and integral representation for
harmonic functions of symmetric stable processes.
J. Funct. Anal. 159 (1998), 267294.
(with R. Song)
 On the existence of
positive solutions for semilinear
elliptic equations with singular lower order coefficients
and Dirichlet boundary conditions.
Math. Ann.
315 (1999), 735769.
(with R.J. Williams and Z. Zhao)
 Intrinsic ultracontractivity, conditional lifetimes
and conditional gauge for symmetric
stable processes on rough domains.
Ill. J. Math. 44 (2000), 138160.
(with R. Song)
 Local time flow related to skew Brownian motion.
Ann. Probab. 29 (2001), 16931715.
(with K. Burdzy)
 Multidimensional symmetric stable processes.
Korean J. Comput. Appl. Math.
6 (1999), 227266
 Crossing estimates for symmetric Markov processes.
Probab. Theory Relat. Fields.
120 (2001), 6884.
(with P.J. Fitzsimmons and R. Song)
 A Note on Green function estimates
for symmetric stable processes.
In Recent Developments in Stochastic Analysis and
Related Topics, p.125135.
Proceedings of the First SinoGerman
Conference on Stochastic Analysis (2002). World Scientific, 2004.
(with R. Song)
 Stochastic differential equations for Dirichlet processes.
Probab. Theory Relat. Fields, 121 (2001), 422446.
(with R. Bass)
 The heat equation in time dependent domains
with insulated boundaries.
J. Math. Anal. Appl.
294 (2004), 581595.
(with K. Burdzy and J. Sylvester)
 Heat equation and reflected Brownian motion
in time dependent domains.
Ann. Probab. 32 (2004), 775804.
(Joint with K. Burdzy and J. Sylvester)
 Heat equation and reflected Brownian motion
in time dependent domains II: Singularities of Solutions.
J. Funct. Anal. 204 (2003), 134.
(with K. Burdzy and J. Sylvester)
 Girsanov and FeynmanKac type
transformations for symmetric Markov processes.
Ann. Inst. Henri Poincare Probab. Statist.,
38 (2002), 475505.
(with T.S. Zhang)
 General gauge and conditional gauge theorems.
Ann. Probab. 30 (2002), 13131339.
(with R. Song)
 Brownian motion with singular drift.
Ann. Probab. 31 (2003), 791817. (with R. Bass)
 Coalescence of synchronous couplings.
Probab. Theory Relat. Fields, 123 (2002), 553578.
(with K. Burdzy)
 Conditional gauge theorem for nonlocal FeynmanKac
transforms.
Probab. Theory Relat. Fields,
125 (2003), 4572.
(with R. Song)
 Gaugeability and conditional gaugeability.
Trans. Amer. Math. Soc.
354 (2002), 46394679.
 Censored stable processes.
Probab. Theory Relat. Fields.
127 (2003), 89152.
(with K. Bogdan and K. Burdzy)
 Hardy inequality for censored stable processes.
Tohoku Math. J. 55 (2003), 439450.
(with R. Song)
 Drift transforms and Green function estimates
for discontinuous processes.
J. Funct. Anal. 201 (2003), 262281.
(with R. Song)
 Green function estimate for censored
stable processes.
Probab. Theory Relat. Fields
124 (2002), 595610.
(with P. Kim)
 Uniqueness for reflecting Brownian motion in lip domains.
Ann. Inst. Henri Poincare Probab. Statist. 41 (2005),
197235.
(with R. Bass and K. Burdzy)
 Analytic characterization of conditional gaugeability
for nonlocal FeynmanKac transforms.
J. Funct. Anal. 202 (2003), 226246.

Absolute continuity of symmetric Markov processes.
Ann. Probab. 32 (2004), 20672098.
(Joint with P.J. Fitzsimmons, M. Takeda, J. Ying and T.S. Zhang)
 Stochastic differential equations driven by
stable processes for which pathwise uniqueness fails.
Stochastic Process Appl. 111 (2004), 115.
(with R. Bass and K. Burdzy)
 Heat kernel estimates for stablelike processes
on dsets.
Stochastic Process Appl. 108 (2003),
2762.
(with T. Kumagai)
 Traps for reflecting Brownian motion.
Math. Z. 252 (2006), 103132. (with K. Burdzy and D. Marshall)
 Stability of Martin boundary
under nonlocal FeynmanKac perturbations.
Probab. Theory Relat. Fields,
128 (2004), 525564.
(with P. Kim)
 Boundary trace of reflecting Brownian motions.
Probab. Theory Relat. Fields,
129 (2004), 117.
(with I. Benjamini and S. Rohde)
 Systems of equations driven by stable processes.
Probab. Theory Relat. Fields, 134 (2006), 175214.
(with R. Bass)
 Onedimensional stochastic differential equations
with singular and degenerate coefficients.
Sankhya 67 (2005), 1945. (with R. Bass)
 Twosided eigenvalue estimates for subordinate processes
in domains.
J. Funct. Anal. 226 (2005),
90113. (with R. Song)

Traces of symmetric Markov processes and their characterizations
Ann. Probab. 34 (2006), 10521102.
(with M. Fukushima and J. Ying)
 Continuity of eigenvalues of
subordinate processes in domains.
Math. Z. 252 (2006), 7189. (with R. Song)
 Synchronous couplings of reflected Brownian motions in smooth domains.
Ill. J. Math. 50 (2006) (Special volume in memory
of Joseph Doob), 189268. (with K. Burdzy and P. Jones)
 Entrance law, exit system and
Levy system of timechanged processes.
Ill. J. Math. 50 (2006) (Special volume in memory
of Joseph Doob), 269312. (with M. Fukushima and J. Ying)
 On the Robin problem in fractal domains.
Proc. London
Math. Soc. 96 (2008), 273311. (with R. F. Bass and K. Burdzy)
 Comparision of potential theoretic properties of
rough domains.
Proc. Amer. Math. Soc. 134 (2006), 32473253.
(with K. Burdzy)
 Shy couplings.
Probab. Theory Relat. Fields, 137 (2007), 345377.
(with I. Benjamini and K. Burdzy)
 Spectral properties of
subordinate processes in domains.
In Stochastic Analysis and Partial Differential Equations,
7784.
(Eds. GQ Chen, E. Hsu and M. Pinsky.)
AMS Compt. Math. 429 (2007).
(with R. Song)
 Extending Markov processes in weak duality
by Poisson point processes of excursions.
Proceedings of the Abel Symposium 2005,
Stochastic Analysis and ApplicationsA Symposium in Honor
of Kiyosi Ito.
(Eds. F.E. Benth, G. Di
Nunno, T. Lindstrom, B. Oksendal and T. Zhang.) Springer, 2007,
pp153196. (with M. Fukushima and J. Ying)
 Pathwise uniqueness for a degenerate
stochastic differential equation.
Ann. Probab. 35 (2007), 23852418.
(with R. Bass and K. Burdzy)
 Heat kernel estimates for jump processes of mixed
types on metric measure spaces.
Probab. Theory Relat. Fields 140 (2008),
277317. (with T. Kumagai)
 Onepoint extensions of Markov processes by darning.
Probab. Theory Relat. Fields 141 (2008), 61112.
(with M. Fukushima)
 Stochastic calculus for symmetric
Markov processes.
Ann. Probab. 36 (2008), 931970.
Errata. Ann. Probab. 40 (2012), 13751376.
(with P. J. Fitzsimmons, K. Kuwae and T.S. Zhang)
 Perturbation of symmetric Markov processes.
Probab. Theory Relat. Fields 140 (2008), 239275.
(with P. J. Fitzsimmons, K. Kuwae and T.S. Zhang)
 Nonlocal Dirichlet forms and symmetric jump processes.
Trans. Amer. Math. Soc. 361 (2009), 19631999.
(with M. T. Barlow, R. F. Bass and M. Kassmann)
 Limit theorems for branching Markov processes.
J. Funct. Anal. 250 (2007), 374399.
(with Y. Shiozawa)
 On Feller's boundary problem
for Markov processes in weak duality.
J. Funct. Anal. 252 (2007), 710733.
(with M. Fukushima)
 Discrete approximations to
reflected Brownian motion.
Ann. Probab. 36 (2008), 698727. (with K. Burdzy)
 On FeynmanKac perturbation of symmetric Markov processes.
In Proceedings of Functional Analysis IX,
Dubrovnik, Croatia, 2005, pp. 3943.
 Interacting superprocesses with
discontinuous spatial motion.
Forum Math. 24 (2012), 11831223.
(with H. Wang and J. Xiong)
 Flux and lateral conditions for symmetric Markov
processes.
Potential Analysis 29 (2008), 241269. (with M. Fukushima)
 SchrammLoewner equations driven by symmetric stable processes.
Comm. Math. Phys. 285 (2009), 799824. (with S. Rohde)
 An almost sure scaling limit theorem for DawsonWatanabe superprocesses
J. Funct. Anal. 254 (2008), 19882019.
(with Y. Ren and H. Wang)
 Exit time, Green function and
semilinear elliptic equations.
Elect. J. Probab. 14 (2009), 5071.
(with R. Atar and S. Athreya)
 Weighted Poincaré inequality
and heat kernel estimates for finite range jump processes.
Math. Ann. 342 (2008), 833883.
(with P. Kim and T. Kumagai)
 Timereversal and elliptic boundary value problems.
Ann. Probab. 37 (2009), 10081043. (with T.S. Zhang)
 On general perturbations of symmetric Markov processes.
J. Math. Pures et
Appliquées 92 (2009), 363374.
(with P. Fitzsimmons, K. Kuwae and T.S. Zhang)
 Stochastic evolution equations driven by stable processes.
Osaka J. Math. 48 (2011), 311327. (with T.S. Zhang)
 Heat kernel estimates for Dirichlet fractional Laplacian.
J. Euro. Math. Soc. 12 (2010), 13071329.
(with P. Kim and R. Song)
 Twosided heat kernel estimates for censored
stablelike processes.
Probab. Theory Relat. Fields 146 (2010), 361399.
(with P. Kim and R. Song)
 Stationary distributions for diffusions with inert drift.
Probab. Theory Relat. Fields 146 (2010), 147.
(with R. Bass, K. Burdzy and M. Hairer)
 On doubly Feller property.
Osaka J. Math. 46 (2009), 909930.
(with K. Kuwae)
 On unique extension of time changed
reflecting Brownian motions.
Ann. Inst. Henri Poincare Probab. Statist.
45 (2009), 864875. (with M. Fukushima)
 A priori Hölder estimate, parabolic Harnack
principle and heat kernel estimates for diffusions with jumps.
Revista Matematica Iberoamericana 26 (2010), 551589.
(with T. Kumagai)
 On notions of harmonicity.
Proc. Amer. Math. Soc. 137 (2009), 34973510.
 On heat kernel estimates and parabolic Harnack inequality for jump
processes on metric measure spaces.
Acta Mathematica Sinica, English Series 25 (2009), 10671086.
(with P. Kim and T. Kumagai)

Symmetric jump processes and their heat kernel estimates.
Sci. China Ser. A. 52 (2009), 14231445.
 Boundary Harnack principle for Δ + Δ^{α/2}.
Trans. Amer. Math. Soc. 384 (2012), 41694205.
(with P. Kim, R. Song and Z. Vondracek)
 Regularity of harmonic functions for a class of singular
stablelike processes.
Math. Z. 266 (2010), 489503. (with R. F. Bass)
 Global heat kernel estimates for fractional Laplacians in unbounded
open sets.
Probab. Theory Relat. Fields.
149 (2011), 373395. (with J. Tokle)
 Sharp heat kernel estimates for relativistic stable processes
in open sets.
Ann. Probab. 40 (2012), 213244.
(with P. Kim and R. Song)
 Green function estimates for relativistic stable processes
in halfspacelike open sets.
Stochastic Process Appl. 121 (2011),
11481172. (with P. Kim and R. Song)
 Dirichlet heat kernel estimates for Δ^{α/2}
+ Δ^{β/2}.
Ill. J. Math. 54 (2010)
(Special issue in honor of D. Burkholder), 13571392.
(with P. Kim and R. Song)
 An L^{2}theory for a class of SPDEs
driven by Lévy processes.
Sci. in China, Series A 55 (2012)
(Special issue on Probability), 22332246.
(with K.H. Kim)
 Sharp Green function estimates for Δ
+ Δ^{α/2} in C^{1,1} open sets
and their applications.
Ill. J. Math.
54 (2010) (Special issue
in honor of D. Burkholder), 9811024.
(with P. Kim, R. Song and Z. Vondracek)
 On subhamonicity for symmetric Markov processes.
J. Math. Soc. Japan, 64 (2012), 11811209. (with K. Kuwae)

Archimedes' principle for Brownian liquid.
Ann. Appl. Probab. 21 (2011), 20532074.
(with K. Burdzy and S. Pal)
 Heat kernel estimates for Δ
+ Δ^{α/2} in C^{1,1} open sets.
J. London Math. Soc. 84 (2011), 5880.
(with P. Kim and R. Song)
 Global heat kernel estimates for symmetric jump processes.
Trans. Amer. Math. Soc. 363 (2011), 50215055.
(with P. Kim and T. Kumagai)
 An L^{p}theory of nondivergence form SPDEs driven
by Lévy processes.
To appear in Forum Math. (with K.H. Kim)
 Discrete approximation of symmetric jump processes on
metric measure spaces.
Probab. Theory Relat. Fields 155 (2013),
703749. (with P. Kim and T. Kumagai)
 Global heat kernel estimate for relativistic stable processes in
halfspacelike open sets.
Potential Analysis. 36 (2012),
235261. (with P. Kim and R. Song)
 Dirichlet heat kernel estimates for fractional Laplacian
under gradient perturbation.
Ann. Probab. 40 (2012), 24832538.
(with P. Kim and R. Song)
 Brownian earthworm.
Ann. Probab. 41 (2013), 40024049.
(with K. Burdzy and S. Pal)
 A localization formula in Dirichlet form theory.
Proc. Amer. Math. Soc. 140 (2012),
18151822. (with M. Fukushima)
 Global heat kernel estimates for
Δ + Δ^{α/2}
in halfspacelike domains.
Eletronic J. Probab.17 (2012),
Paper 32, 131.
(with P. Kim and R. Song)
 Uniform integrability of exponential martingales and
spectral bounds of nonlocal FeynmanKac semigroups.
In Stochastic Analysis and Applications to Finance,
Essays in Honor of Jiaan Yan. (Eds by T. Zhang and X. Zhou), 2012.
pp.5575.
 Reflecting random walk in fractal domains.
Ann. Probab. 41 (2013), 24013050.
(with K. Burdzy)
 L^{p}independence of
spectral bounds of generalized nonlocal FeynmanKac semigroups
J. Funct. Anal. 262 (2012), 41204139.
 Spacetime fractional diffusion on bounded
domains.
J. Math. Anal. Appl. 393 (2012),
479488.
(with M. M. Meerschaert and E. Nane)
 Global heat kernel estimate for relativistic stable
processes in exterior open sets.
J. Funct. Anal. 263 (2012), 448475.
(with P. Kim and R. Song)
 Stability of Dirichlet heat kernel estimates for nonlocal
operators under FeynmanKac perturbation.
To appear in Trans. Amer. Math. Soc. (with P. Kim and R. Song)
 A probabilistic approach to mixed boundary value problems
for elliptic operators with singular coefficients.
Proc. Amer. Math. Soc. 142 (2014),21352149.
(with T. Zhang)
 Perturbation by nonlocal operators.
Preprint 2012. (with Jieming Wang)
 Chordal KomatuLoewner equation and Brownian motion with darning
in multiply connected domains.
To appear in Trans. Amer. Math. Soc.
(with M. Fukushima and S. Rohde)
 Dirichlet heat kernel estimates for rotationally symmetric
L\'evy processes.
To appear in Proc. London Math. Soc.(with P. Kim and R. Song)
 Dirichlet heat kernel estimates for subordinate Brownian motions
with Gaussian components.
To appear in J. Reine Angew. Math..
(with P. Kim and R. Song)
 Uniqueness of stable processes with drifts.
Preprint 2013. (with L. Wang)
 Quenched invariance principles for random walks and
elliptic diffusions in random media with boundary.
To appear in Ann. Probab. (with D.A. Croydon and T. Kumagai)
 On uniform positivity of transition densities of
small noise constrained diffusions.
Electron. Commun. Probab. 19 (2014), no. 1, p.19.
(with A. Budhiraja)
 Heat kernels and analyticity of nonsymmetric
jump diffusion semigroups.
Preprint 2013. (with X. Zhang)
 Onedimensional heat equation with discontinuous conductance.
To appear in Sci. China Math. (with M. Zili)
 Ergodicity for time changed symmetric stable processes.
To appear in Stochastic Process Appl. (with Jian Wang)
 Hydrodynamic limits and propagation of chaos for interacting random walks in
domains.
Preprint 2014. (with W.T. Fan)
 Systems of interacting diffusions with partial annihilation through membranes.
Preprint 2014. (with W.T. Fan)
 Fractional time stochastic partial differential equations.
Preprint 2014. (with K.H. Kim and P. Kim)
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