PUBLICATIONS
Zhen-Qing Chen
- Stochastic analysis on the extended sample space and tightness results.
Probab. Theory Relat. Fields, 86 (1990), 517-549.
- On reflected Dirichlet spaces.
Probab. Theory Relat. Fields, 94 (1992), 135-162.
- Pseudo Jordan domains and reflecting Brownian motions.
Probab. Theory Relat. Fields, 94 (1992), 271-280.
- On reflecting diffusion processes and Skorokhod decompositions.
Probab. Theory Relat. Fields, 94 (1993), 281-316.
- Reflecting Brownian motions: quasimartingales and strong Caccioppoli sets.
Potential Analysis, 2 (1993), 219-243. (with P.J. Fitzsimmons and R.J. Williams)
- The binding capacity is a probability density function.
Biophysical Journal, 65 (1993), 164-170. (with E. DiCera)
- Switched diffusion processes and systems of elliptic equations--a Dirichlet space approach.
Proc. Royal Soc. Edinburgh, 124A (1994), 673-701. (with Z. Zhao)
- 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)
- 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)
- Quasi-homeomorphisms of Dirichlet forms.
Nagoya J. Math. 136 (1994), 1-15. (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), 323-357. (with Z. Zhao)
- 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)
- 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)
- Reflecting Brownian motions and a deletion result for Sobolev spaces of order (1,2).
Potential Analysis, 5 (1996). 383-401.
- Potential theory for elliptic systems.
Ann. Probab. 24 (1996), 293-319. (with Z. Zhao)
- Holomorphic diffusions and boundary behavior of harmonic functions.
Ann. Probab. 25 (1997), 1103-1134. (with R. Durrett and G. Ma)
- Harnack principle for weakly coupled elliptic systems.
Journal of Differential Equations, 139 (1997), 261-282. (with Z. Zhao)
- Stability and approximations of symmetric diffusion semigroups and kernels.
J. Funct. Anal. 152 (1998), 255-280. (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), 465-501. (with R. Song)
- Intrinsic ultracontractivity and conditional gauge for symmetric stable processes.
J. Funct. Anal. 150 (1997), 204-239. (with R. Song)
- Weak convergence of reflecting Brownian motions.
Elect. Comm. Probab. 3 (1998), 29-33. (with K. Burdzy)
- Martin boundary and integral representation for harmonic functions of symmetric stable processes.
J. Funct. Anal. 159 (1998), 267-294. (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), 735--769. (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), 138--160. (with R. Song)
- Local time flow related to skew Brownian motion.
Ann. Probab. 29 (2001), 1693--1715. (with K. Burdzy)
- Multidimensional symmetric stable processes.
Korean J. Comput. Appl. Math. 6 (1999), 227-266.
- Crossing estimates for symmetric Markov processes.
Probab. Theory Relat. Fields. 120 (2001), 68-84. (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.125-135.
Proceedings of the First Sino-German Conference on Stochastic Analysis (2002). World Scientific, 2004. (with R. Song)
- Stochastic differential equations for Dirichlet processes.
Probab. Theory Relat. Fields, 121 (2001), 422-446. (with R. Bass)
- The heat equation in time dependent domains with insulated boundaries.
J. Math. Anal. Appl. 294 (2004), 581-595. (with K. Burdzy and J. Sylvester)
- Heat equation and reflected Brownian motion in time dependent domains.
Ann. Probab. 32 (2004), 775-804. (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), 1-34. (with K. Burdzy and J. Sylvester)
- Girsanov and Feynman-Kac type transformations for symmetric Markov processes.
Ann. Inst. Henri Poincare Probab. Statist., 38 (2002), 475-505. (with T.-S. Zhang)
- General gauge and conditional gauge theorems.
Ann. Probab. 30 (2002), 1313-1339. (with R. Song)
- Brownian motion with singular drift.
Ann. Probab. 31 (2003), 791-817. (with R. Bass)
- Coalescence of synchronous couplings.
Probab. Theory Relat. Fields, 123 (2002), 553--578. (with K. Burdzy)
- Conditional gauge theorem for non-local Feynman-Kac transforms.
Probab. Theory Relat. Fields, 125 (2003), 45-72. (with R. Song)
- Gaugeability and conditional gaugeability.
Trans. Amer. Math. Soc. 354 (2002), 4639--4679.
- Censored stable processes.
Probab. Theory Relat. Fields. 127 (2003), 89--152. (with K. Bogdan and K. Burdzy)
- Hardy inequality for censored stable processes.
Tohoku Math. J. 55 (2003), 439-450. (with R. Song)
- Drift transforms and Green function estimates for discontinuous processes.
J. Funct. Anal. 201 (2003), 262-281. (with R. Song)
- Green function estimate for censored stable processes.
Probab. Theory Relat. Fields 124 (2002), 595-610. (with P. Kim)
- Uniqueness for reflecting Brownian motion in lip domains.
Ann. Inst. Henri Poincare Probab. Statist. 41 (2005), 197-235. (with R. Bass and K. Burdzy)
- Analytic characterization of conditional gaugeability for non-local Feynman-Kac transforms.
J. Funct. Anal. 202 (2003), 226-246.
- 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)
- 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)
- Heat kernel estimates for stable-like processes on d-sets.
Stochastic Process Appl. 108 (2003), 27-62. (with T. Kumagai)
- Traps for reflecting Brownian motion.
Math. Z. 252 (2006), 103-132. (with K. Burdzy and D. Marshall)
- Stability of Martin boundary under non-local Feynman-Kac perturbations.
Probab. Theory Relat. Fields, 128 (2004), 525-564. (with P. Kim)
- Boundary trace of reflecting Brownian motions.
Probab. Theory Relat. Fields, 129 (2004), 1-17. (with I. Benjamini and S. Rohde)
- Systems of equations driven by stable processes.
Probab. Theory Relat. Fields, 134 (2006), 175-214. (with R. Bass)
- One-dimensional stochastic differential equations with singular and degenerate coefficients.
Sankhya 67 (2005), 19-45. (with R. Bass)
- Two-sided eigenvalue estimates for subordinate processes in domains.
J. Funct. Anal. 226 (2005), 90-113. (with R. Song)
- Traces of symmetric Markov processes and their characterizations.
Ann. Probab. 34 (2006), 1052-1102. (with M. Fukushima and J. Ying)
- Continuity of eigenvalues of subordinate processes in domains.
Math. Z. 252 (2006), 71-89. (with R. Song)
- 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)
- 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)
- On the Robin problem in fractal domains.
Proc. London Math. Soc. 96 (2008), 273-311. (with R. F. Bass and K. Burdzy)
- Comparison of potential theoretic properties of rough domains.
Proc. Amer. Math. Soc. 134 (2006), 3247-3253. (with K. Burdzy)
- Shy couplings.
Probab. Theory Relat. Fields, 137 (2007), 345-377. (with I. Benjamini and K. Burdzy)
- 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)
- 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)
- Pathwise uniqueness for a degenerate stochastic differential equation.
Ann. Probab. 35 (2007), 2385-2418. (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), 277-317. (with T. Kumagai)
- One-point extensions of Markov processes by darning.
Probab. Theory Relat. Fields 141 (2008), 61-112. (with M. Fukushima)
- 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)
- Perturbation of symmetric Markov processes.
Probab. Theory Relat. Fields 140 (2008), 239-275. (with P. J. Fitzsimmons, K. Kuwae and T.-S. Zhang)
- 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)
- Limit theorems for branching Markov processes.
J. Funct. Anal. 250 (2007), 374-399. (with Y. Shiozawa)
- On Feller's boundary problem for Markov processes in weak duality.
J. Funct. Anal. 252 (2007), 710-733. (with M. Fukushima)
- Discrete approximations to reflected Brownian motion.
Ann. Probab. 36 (2008), 698-727. (with K. Burdzy)
- On Feynman-Kac perturbation of symmetric Markov processes.
In Proceedings of Functional Analysis IX, Dubrovnik, Croatia, 2005, pp. 39-43.
- Interacting superprocesses with discontinuous spatial motion.
Forum Math. 24 (2012), 1183-1223. (with H. Wang and J. Xiong)
- Flux and lateral conditions for symmetric Markov processes.
Potential Analysis 29 (2008), 241-269. (with M. Fukushima)
- Schramm-Loewner equations driven by symmetric stable processes.
Comm. Math. Phys. 285 (2009), 799-824. (with S. Rohde)
- An almost sure scaling limit theorem for Dawson-Watanabe superprocesses
J. Funct. Anal. 254 (2008), 1988-2019. (with Y. Ren and H. Wang)
- Exit time, Green function and semilinear elliptic equations.
Elect. J. Probab. 14 (2009), 50-71. (with R. Atar and S. Athreya)
- Weighted Poincaré inequality and heat kernel estimates for finite range jump processes.
Math. Ann. 342 (2008), 833-883. (with P. Kim and T. Kumagai)
- Time-reversal and elliptic boundary value problems.
Ann. Probab. 37 (2009), 1008-1043. (with T.-S. Zhang)
- 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)
- Stochastic evolution equations driven by stable processes.
Osaka J. Math. 48 (2011), 311-327. (with T.-S. Zhang)
- Heat kernel estimates for Dirichlet fractional Laplacian.
J. Euro. Math. Soc. 12 (2010), 1307-1329. (with P. Kim and R. Song)
- Two-sided heat kernel estimates for censored stable-like processes.
Probab. Theory Relat. Fields 146 (2010), 361-399. (with P. Kim and R. Song)
- Stationary distributions for diffusions with inert drift.
Probab. Theory Relat. Fields 146 (2010), 1-47. (with R. Bass, K. Burdzy and M. Hairer)
- On doubly Feller property.
Osaka J. Math. 46 (2009), 909-930. (with K. Kuwae)
- On unique extension of time changed reflecting Brownian motions.
Ann. Inst. Henri Poincare Probab. Statist. 45 (2009), 864-875. (with M. Fukushima)
- 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)
- On notions of harmonicity.
Proc. Amer. Math. Soc. 137 (2009), 3497-3510.
- 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)
- Symmetric jump processes and their heat kernel estimates.
Sci. China Ser. A. 52 (2009), 1423-1445.
- Boundary Harnack principle for Δ + Δ^{α/2}.
Trans. Amer. Math. Soc. 384 (2012), 4169-4205. (with P. Kim, R. Song and Z. Vondracek)
- Regularity of harmonic functions for a class of singular stable-like processes.
Math. Z. 266 (2010), 489-503. (with R. F. Bass)
- Global heat kernel estimates for fractional Laplacians in unbounded open sets.
Probab. Theory Relat. Fields. 149 (2011), 373-395. (with J. Tokle)
- Sharp heat kernel estimates for relativistic stable processes in open sets.
Ann. Probab. 40 (2012), 213-244. (with P. Kim and R. Song)
- 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)
- Dirichlet heat kernel estimates for Δ ^{α/2}
+Δ ^{β/2} .
Ill. J. Math. 54 (2010) (Special issue in honor of D. Burkholder), 1357-1392. (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), 2233-2246. (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), 981-1024. (with P. Kim, R. Song and Z. Vondracek)
- On subhamonicity for symmetric Markov processes.
J. Math. Soc. Japan, 64 (2012), 1181-1209. (with K. Kuwae)
- Archimedes' principle for Brownian liquid.
Ann. Appl. Probab. 21 (2011), 2053-2074. (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), 58-80. (with P. Kim and R. Song)
- Global heat kernel estimates for symmetric jump processes.
Trans. Amer. Math. Soc. 363 (2011), 5021-5055. (with P. Kim and T. Kumagai)
- An L^{p}-theory of non-divergence form SPDEs driven by Lévy processes.
Forum Math. 26 (2014), 1381-1411. (with K.-H. Kim)
- Discrete approximation of symmetric jump processes on metric measure spaces.
Probab. Theory Relat. Fields 155 (2013), 703-749. (with P. Kim and T. Kumagai)
- 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)
- Dirichlet heat kernel estimates for fractional Laplacian under gradient perturbation.
Ann. Probab. 40 (2012), 2483-2538. (with P. Kim and R. Song)
- Brownian earthworm.
Ann. Probab. 41 (2013), 4002-4049. (with K. Burdzy and S. Pal)
- A localization formula in Dirichlet form theory.
Proc. Amer. Math. Soc. 140 (2012), 1815-1822. (with M. Fukushima)
- Global heat kernel estimates for Δ + Δ^{α/2} in half-space-like domains.
Eletronic J. Probab.17 (2012), Paper 32, 1-31. (with P. Kim and R. Song)
- 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.
- Reflecting random walk in fractal domains.
Ann. Probab. 41 (2013), 2401-3050. (with K. Burdzy)
- L^{p}-independence of spectral bounds of generalized non-local Feynman-Kac semigroups
J. Funct. Anal. 262 (2012), 4120-4139.
- Space-time fractional diffusion on bounded domains.
J. Math. Anal. Appl. 393 (2012), 479-488. (with M. M. Meerschaert and E. Nane)
- 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)
- Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation.
Trans. Amer. Math. Soc. 367 (2015), 5237-5270. (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), 2135-2149. (with T. Zhang)
- Perturbation by non-local operators.
To appear in Ann. Inst. Henri Poincaré Probab. Statist. (with Jieming Wang)
- Chordal Komatu-Loewner equation and Brownian motion with darning in multiply connected domains.
Trans. Amer. Math. Soc. 368 (2016), 4065-4114.
(with M. Fukushima and S. Rohde)
- Dirichlet heat kernel estimates for rotationally symmetric Lévy processes.
Proc. London Math. Soc. 109 (2014), 90-120. (with P. Kim and R. Song)
- Dirichlet heat kernel estimates for subordinate Brownian motions with Gaussian components.
J. Reine Angew. Math.. 711 (2016), 111-138. (with P. Kim and R. Song)
- Uniqueness of stable processes with drifts.
Proc. Amer. Math. Soc. 144 (2016), 2661-2675. (with L. Wang)
- Quenched invariance principles for random walks and elliptic diffusions in random media with boundary.
Ann. Probab. 43 (2015), 1594-1642. (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.1-9. (with A. Budhiraja)
- Heat kernels and analyticity of non-symmetric jump diffusion semigroups.
Probab. Theory Relat. Fields 165 (2016), 267-312. (with X. Zhang)
- One-dimensional heat equation with discontinuous conductance.
Sci. China Math. 58 (2015), 97-108. (with M. Zili)
- Ergodicity for time changed symmetric stable processes.
Stochastic Process Appl. 124 (2014), 2799-2823. (with Jian Wang)
- Hydrodynamic limits and propagation of chaos for interacting random walks in domains.
To appear in Ann. Appl. probab. (with W.-T. Fan)
- Systems of interacting diffusions with partial annihilation through membranes.
Ann. Probab. 45 (2017), 100-146. (with W.-T. Fan)
- Fractional time stochastic partial differential equations.
Stochastic Process Appl. 125 (2015), 1470-1499. (with K.-H. Kim and P. Kim)
- One-point reflection.
Stochastic Process Appl. 125 (2015), 1368-1393. (with M. Fukushima)
- Functional central limit theorem for Brownian particles in domains with Robin boundary condition.
J. Funct. Anal. 269 (2015), 3765-3811. (with W.-T. Fan)
- Scaling limits of interacting diffusions in domains.
Front. Math. China 9 (2014), 717-736. (with W.-T. Fan)
- Stochastic Komatu-Loewner evolutions and BMD domain constant.
Preprint 2014. (with M. Fukushima)
- Fluctuation limit for interacting diffusions with partial annihilations through membranes.
J. Stat. Phys. 164 (2016), 890-936. (with W.-T. Fan)
- Heat kernel estimates for Δ + Δ^{α/2} under gradient perturbation.
Stochastic Processes Appl. 125 (2015), 2603-2642. (with E. Hu)
- Hölder estimates for nonlocal-diffusion equations with drifts.
Commun. Math. Stat. 2 (2014), 331-348. (with X. Zhang)
- Global Dirichlet heat kernel estimates for symmetric Lévy processes in half-space.
Acta Applicandae Mathematicae 146 (2016), 113-143. (with P. Kim)
- Drift perturbation of subordinate Brownian motions with Gaussian component.
Sci. China Math. 59 (2016), 239-260. (with X. Dou)
- Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators.
Potential Analysis 45 (2016), 509-537. (with Y.-X. Ren and T. Yang)
- Stochastic flows for Lévy processes with Hölder drifts.
To appear in Revista Matemática Iberoamericana. (with R. Song and X. Zhang)
- Strong law of large numbers for supercritical superprocesses under second moment condition.
Front. Math. China 10 (2015), 807-838.
(with Y. Ren, R. Song and R. Zhang)
- Law of large numbers for branching symmetric Hunt processes with
measure-valued branching rates.
To appear in J. Theor. Probab. (with Y.-X. Ren and T. Yang)
- Obliquely reflected Brownian motion.
To appear in Ann. Probab. (with K. Burdzy, D. Marshall and K. Ramanan)
- Dirichlet heat kernel estimates for fractional Laplacian under non-local perturbation.
Preprint 2016. (with Ting Yang)
- Stability of heat kernel estimates
for symmetric jump processes on metric measure spaces.
Preprint 2016. (with T. Kumagai and J. Wang)
- Brownian motion on spaces with varying dimension.
Preprint 2016. (with S. Lou)
- Stochastic Komatu-Loewner evolutions and SLEs.
To appear in Stochastic Process Appl. (with M. Fukushima and H. Suzuki)
- Strong stability of heat kernels of non-symmetric stable-like operators.
To appear in Stochastic Analysis and Related Topics,
A Festschrift in honor of Rodrigo Banuelos.
Progress in Probability, Birkhauser. (with X. Zhang)
- Properties of switching jump diffusions:
maximum principles and Harnack inequalities.
Preprint 2016. (with X. Chen, K. Tran and G. Yin)
- L^{p}-maximal hypoelliptic regularity of nonlocal kinetic Fokker-Planck operators.
Preprint 2016. (with X. Zhang)
- Stability of parabolic Harnack inequalities
for symmetric non-local Dirichlet forms.
Preprint 2016. (with T. Kumagai and J. Wang)
- Reflections at infinity of time changed RBMs
on domains with Liouville branches.
To appear in J. Math. Soc. Japan. (with M. Fukushima)
- Heat kernels for non-symmetric diffusions operators with jump.
Preprint 2016. (with E. Hu, L. Xie and X. Zhang)
- Markov processes with darning and their approximations.
Preprint 2017. (with J. Peng)
- Time fractional equations and probabilistic representation.
To appear in Chaos, Solitons and Fractals.
- Heat kernels for non-symmetric non-local operators.
To appear as a book chapter in Recent Developments in the
Nonlocal Theory. De Gruyter. (with X. Zhang).