教授

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张希承

个人简介


图片4.jpgPersonal Information

Name: Xicheng Zhang (张希承)

Born: 1973/08/03, Hubei, China

Email: xczhang.math@bit.edu.cn

Institute: School of Mathematics and Statistics, BIT, 100081, P.R. China

Address: No.5 Zhongguancun South Street, Haidian District, Beijing, P.R. China


Educational Background

► 09/1995--06/2000, PhD in Mathematics, Huazhong University of Science and Technology. Supervisor: Prof. Jiagang Ren. Major: Stochastic Analysis.

09/1991--07/1995, Bachelor in Mathematics, Huazhong University of Science and Technology, China


Working Experience

06/2022--Present, Professor(教授,博导), School of Mathematics and Statistics, Beijing Institute of Technology

04/2010--06/2022, Professor, School of Mathematics and Statistics, Wuhan University

01/2000--04/2010, Lecturer, Associated Professor, Professor, School of Mathematics and Statistics, Huazhong University of Science and Technology


Teachings

Probability, Stochastic Processes, Stochastic Analysis, Measure Theory, Stochastic Differential Equations


Publications

n X. Zhang; R. Zhu; X. Zhu: Singular HJB equations with applications to KPZ on the real line. Probab. Theory Related Fields http:// doi.org/10.1007/s00440-022-01137-w.

n S. Menozzi; X. Zhang: Heat kernel of supercritical nonlocal operators with unbounded drifts. J. Éc. polytech. Math. 9 (2022), 537–579.

n Z. Hao; X. Peng; X. Zhang: Hörmander's hypoelliptic theorem for nonlocal operators. J. Theoretical Probab. 34 (2021), no. 4, 1870–1916.

n Z.Q. Chen; X. Zhang; G. Zhao: Supercritical SDEs driven by multiplicative stable-like Lévy processes. Trans. Amer. Math. Soc. 374 (2021), no. 11, 7621–7655.

n Z. Hao; M. Röckner; X. Zhang: Euler scheme for density dependent stochastic differential equations. J. Differential Equations 274, 996–1014(2021).

n X. Zhang; G. Zhao: Guohuan Stochastic Lagrangian path for Leray's solutions of 3D Navier-Stokes equations. Comm. Math. Phys. 381 (2021), no. 2, 491–525.

n S. Menozzi; A. Pesce; Zhang X: Density and gradient estimates for non-degenerate Brownian SDEs with unbounded measurable drift. J. Differential Equations 272, 330–369(2021).

n Z.Q. Chen; Z. Hao; X. Zhang: Hölder regularity and gradient estimates for SDEs driven by cylindrical α-stable processes. Electron. J. Probab. 22, Paper no. 137, 23 pp(2020).

n M. Röckner; L. Xie; X. Zhang: Superposition principle for non-local Fokker-Planck-Kolmogorov operators. Probab. Theory Related Fields 178, no. 3-4, 699–733(2020).

n Z. Hao; M. Wu; X. Zhang: Schauder estimates for nonlocal kinetic equations and applications. J. Math. Pures Appl. (9) 140, 139–184(2020).

n P. Xia; L. Xie; X. Zhang; G. Zhao: $L^q(L^p)$-theory of stochastic differential equations. Stochastic Process. Appl. 130, no. 8, 5188–5211(2020).

n L. Xie; X. Zhang: Ergodicity of stochastic differential equations with jumps and singular coefficients. Ann. Inst. Henri Poincaré Probab. Stat. 56, no. 1, 175–229(2020).

n Z. Wang; X. Zhang: Existence and uniqueness of degenerate SDEs with Hölder diffusion and measurable drift. J. Math. Anal. Appl. 484, no. 1, 123679, 11pp (2020).

n X. Zhang: A discretized version of Krylov’s estimate and its applications. Electron. J. Probab. 24, no. 131, 1-17(2019).

n K. Du; X. Zhang: Optimal gradient estimates of heat kernels of stable-like operators. Proc. Amer. Math. Soc. 147, 3559-3565(2018).

n Z.Q. Chen; R. Song; X. Zhang: Stochastic flows for Levy processes with Holder drifts. Rev. Mat. Iberoam. 34, no. 4, 1755-1788(2018).

n Z.Q. Chen; X. Zhang: $L^p$-maximal hypoelliptic regularity of nonlocal kinetic Fokker–Planck operators. J. Math. Pures Appl. 116, 52–87(2018).

n X. Zhang: Stochastic Hamiltonian flows with singular coefficients. Science China Mathematics 61, no. 8: 1353–1384(2018).

n Z.Q. Chen; E. Hu; L. Xie; X. Zhang: Heat kernels for non-symmetric diffusion operators with jumps. J. Differential Equations 263, 6576-6634(2017).

n Y. Xie; X. Zhang: Stochastic integrals and BDG's inequalities in Orlicz-type spaces. Stochastic Process. Appl. 127, 3228-3250(2017).

n X. Zhang: Fundamental solutions of nonlocal Hormander's operators II. Annals of Probability 45, no. 3, 1799-1841(2017).

n X. Zhang: Stochastic differential equations with Sobolev diffusion and singular drifts and applications. Annals of Applied Probab. 26, no. 5, 2697-2732(2016).

n L. Xie; X. Zhang: Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients. Annals of Probab. 44, 6, 3661-3687(2016).

n X. Zhang: Fundamental Solutions of Nonlocal Hörmander’s Operators. Commun. Math. Stat. 4: 359-402(2016).

n F.Y. Wang; X. Zhang: Degenerate SDE with Hodler-Dini drift and non-Lipschitz noise coefficient. SIAM J. Math. Anal. 48, no. 3, pp. 2189-2222(2016).

n Z. Dong; X. Peng; Y. Song; X. Zhang: Strong Feller properties for degenerate SDEs with jumps. Ann. Inst. Henri Poincaré Probab. Stat. 52, no. 2, 888-897(2016).

n Z.Q. Chen; X. Zhang: Heat kernels and analyticity of non-symmetric jump diffusion semigroups. Probability Theory and Related Fields 165:267-312(2016).

n F.Y. Wang; X. Zhang: Degenerate SDEs in Hilbert Spaces with Rough Drifts. Infin. Dimens. Anal. Quantum Probab. Relat. 18, no. 4, 1550026, 25 pp(2015).

n F.Y. Wang; L. Xu; X. Zhang: Gradient estimates for SDEs Driven by Multiplicative Levy Noise. J. Funct. Anal. 269, no. 10, 3195-3219(2015).

n L. Wang; X. Zhang: Harnack inequalities of SDEs driven by cylindrical $\alpha$-stable processes. Potential Anal. 42, no. 3, 657-669(2015).

n L. Wang; L. Xie; X. Zhang: Derivative formulae for SDEs driven by multiplicative $\alpha$-stable-like processes. Stochastic Process. Appl. (125): 867-885(2015).

n F.Y. Wang; X. Zhang: Heat kernel for fractional diffusion operators with perturbations. Forum Mathematicum 27, 973-994(2015).

n Y. Song; X. Zhang: Regularity of density for SDEs driven by degenerate Levy noises. Electronic Journal of Probability 20, no. 21, 1-27(2015).

n Z.Q. Chen; X. Zhang: Holder estimates for nonlocal-diffusion equations with drifts. Commun. Math. Stat. 2, 3, 331-348(2014).

n L. Xie; X. Zhang: Heat kernel estimates for critical fractional diffusion operators. Studia Math. 224 (3), 221-263(2014).

n X. Zhang: Fundamental solution of kinetic Fokker-Planck operator with anisotropic nonlocal dissipativity. SIAM Journal of Mathematical Analysis 46, no. 3, 2254-2280(2014).

n X. Zhang: Densities for SDEs driven by degenerate $\alpha$-stable processes. Annals of Prob. 42, no. 5, 1885-1910(2014).

n Z. Dong; L. Xu; X. Zhang: Exponential ergodicity of stochastic Burgers equations driven by $\alpha$-stable processes. Journal of Statistics Physics 15, 929-949(2014).

n X. Zhang: $L^p$-maximal regularity of nonlocal parabolic equations and applications. Annales de l'Institut Henri Poincar\'e (C) Non-linerar\'e. 30, 573-614 (2013).

n F.Y. Wang; X. Zhang: Derivative formula and applications for degenerate diffusion semigroups. J. Math. Pures Appl. 99, no. 6, 726-740(2013).

n X. Zhang: Degenerate irregular SDEs with jumps and application to integro-differential equations of Fokker-Planck type. Electron. J. Probab.18, 55, 1-25(2013).

n X. Zhang: Stochastic differential equations with Sobolev drifts and driven by Levy processes. Ann. Inst. Henri Poincaré Probab. Stat. 49, No. 4, 1057-1079(2013).

n X. Zhang: Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients. Rev. Mate. Ibv. 29, no.1, 25-52(2013).

n X. Zhang: Derivative formula and gradient estimate for SDEs driven by $\alpha$-stable processes. Stochastic Process. Appl. 123, 4, 1213-1228(2013).

n X. Zhang: Stochastic Monge-Kantorovich problem and its duality. Stochastic and Stochastic Reports 85, 1, 71-84(2013).

n X. Zhang: Well-posedness of fully nonlinear and nonlocal critical parabolic equations. Journal of Evolution Equations 13, 1, 135-162 (2013).

n X. Zhang: Stochastic Lagrangian particle approach to fractal Navier-Stokes equations. Comm. in Math Phys. 311, 1, 133-155(2012).

n J. Wang; X. Zhang: Probabilistic approach for systems of second order quasi-linear parabolic PDEs. J. Math. Anal. Appl. 388, no.2, 676-694(2012).

n X. Zhang: Stochastic functional differential equations driven by L\'evy processes and quasi-linear partial integro-differential equations. Ann. of Appl. Probab. 22, no. 6, 2505-2538(2012).

n X. Zhang: Stochastic partial differential equations with unbounded and degenerate coefficients. J. Diff. Equa. 250, 1924-1966(2011).

n J. Ren; X. Zhang: Limit theorem for stochastic differential equations with discontinuous coefficients. SIAM J. Math. Anal. 43, no. 1, 302-321(2011).

n X. Zhang: Stochastic homeomorphism flows of SDEs with singular drifts and Sobolev diffusion coefficients. Electron. J. Probab.16, no. 38,1096-1116(2011).

n X. Zhang: Quasi-invariant stochastic flows of SDEs with non-smooth drifts on compact manifolds. Stoch. Proc. Appl. 121, 1373-1388(2011).

n Z. Dong; L. Xu; X. Zhang: Invariant measures of stochastic 2$d$ Navier-Stokes equations driven by $\alpha$-stable processes. Elect. Comm. in Probab. 16, 678-688(2011).

n X. Zhang: Stochastic flows of SDEs with irregular coefficients and stochastic transport equations. Bull. Sci. Math. France 134, 340-378(2010).

n X. Zhang: A stochastic representation for backward incompressible Navier-Stokes equations. Prob. Theory and Rela. Fields 148, no. 1-2, 305-332(2010).

n J. Ren; S. Xu; X. Zhang: Large deviations for multi-valued stochastic differential equations. Journal of Theoretical Probability 23, no. 4, 1142-1156(2010).

n X. Zhang: Stochastic flows and Bismut formulas for non-linear growth stochastic Hamiltonian systems. Stochastic Process. Appl. 120, no. 10, 1929-1949(2010).

n X. Zhang: Smooth Solutions of Stochastic partial differential equations driven by multiplicative noises. Science in China: Mathematics 53, no. 11, 2949-2972(2010).

n M. Röckner; X. Zhang: Weak uniqueness of Fokker-Planck equations with degenerate and bounded coefficients. Comptes Rendus Mathematique 348, 435-438(2010).

n J. Ren; J. Wu; X. Zhang: Exponential ergodicity of multi-valued stochastic differential equations. Bull. Sci. Math. France 134, 391-404(2010).

n X. Zhang: Stochastic Volterra equations in Banach spaces and stochastic partial differential equations. J. Fun. Anal. 258, 4, 15, Pages 1361-1425(2010).

n M. Röckner; T. Zhang; X. Zhang: Large deviations for stochastic tamed 3D Navier-Stokes equations. Applied Mathematics and Optimization 61, 267-285(2010).

n X. Zhang: Exponential ergodicity of non-Lipschitz stochastic differential equations. Proc. Amer. Math. Soc. 137, 317-327(2009).

n B. Goldys; M. Röckner; X. Zhang: Martingale solutions and Markov selections for stochastic partial differential equations. Stochastic Process. Appl. 119, 5, 1725-1764(2009).

n X. Zhang: Clark-Ocone formula and variational representation for Poisson functionals. Annals of Prob. 37, no. 2, 506-529(2009).

n M. Röckner; X. Zhang: Stochastic tamed 3D Navier-Stokes equations: existence, uniqueness and ergodicity. Prob. Theory and Rela. Fields 145, no. 1-2, 211-267(2009).

n X. Zhang: A tamed 3D Navier-Stokes equation in uniform C^2-domains. Nonlinear Analysis: Theory, Methods and Applications 71, 3093-3112(2009).

n X. Zhang: A variational representation for random functionals on abstract Wiener spaces. J. Math. Kyoto Univ. 49(3), 475-490(2009).

n X. Zhang: On stochastic evolution equations with non-Lipschitz coefficients. Stochastic and Dynamics 9, No. 4, 549-595(2009).

n M. Röckner; X. Zhang: Tamed 3D Navier-Stokes equation: existence, uniqueness and regularity. Infinite Dimensional Analysis and Quantum Probability 12, no. 4, 525-549(2009).

n X. Zhang: Euler schemes and large deviations for stochastic Volterra equations with singular kernels. J. of Differential Equation 244, 2226-2250(2008).

n J. Ren; X. Zhang: Freidlin-Wentzell's large deviations for stochastic evolution equations. J. Funct. Anal. 254, 3148-3172(2008).

n X. Zhang: A regularity criterion for the solutions of 3D Navier-Stokes equations. J. Math. Analysis and Appl. 346, 336-339(2008).

n H. Qiao; X. Zhang: Homeomorphism flows for non-Lipschitz stochastic differential equations with jumps. Stoch. Proc. and Appl.118, 2254-2268(2008).

n X. Zhang: Variational approximation of Fokker-Planck equation on Riemannian manifold. Prob. Theory and Rela. Fields 137, no. 3, 519-539(2007).

n H. Qiao; X. Zhang: Homeomorphism of solutions to backward SDEs and applications. Stochastic Process. Appl. 117, 3, 399-408(2007).

n X. Zhang: Skorohod problem and multivalued stochastic evolution equations in Banach spaces. Bull. Sci. Math. France 131, 175-217(2007).

n J. Ren; M. Röckner; X. Zhang: Kusuoka-Stroock formula on configuration space and regularities of local times with jumps. Potential Analysis 26, no. 4, 363-396(2007).

n J. Ren; X. Zhang: Regularity of local times of random fields. J. Fun. Anal. 249, 1, 199-219(2007).

n X. Zhang: Regularities for semilinear stochastic partial differential equations. J. Fun. Anal. 249, 15 August 2007, Pages 454-476(2007).

n X. Zhang; X. Zhang: Probability approaches to spatially homogeneous Boltzmann equations. Stochastic Analysis and Applications 25, 1129-1150(2007).

n Z. Wang; X. Zhang: Non-Lipschitz backward stochastic Volterra type equations with jumps. Stochastic and Dynamics 7, no. 4, 479--496(2007).

n X. Zhang: Relatively compact families of functionals on abstract Wiener space and applications. J. Func. Anal. 232, 1, 195-221(2006).

n X. Zhang: Euler-Maruyama approximations for SDEs with non-Lipschitz coefficients and applications. J. Math. Anal. and Appl. 316, 2, 447-458.

n X. Zhang: Relatively compact criterions of Hilbert valued random fields on abstract Wiener space. C. R. Math. Acad. Sci. Paris 342, 6, 437-440(2006).

n J. Ren; X. Zhang: Topologies on homeomorphism spaces of certain metric spaces. J. Math. Anal. and Appl. 316, 2, 42-46.

n X. Zhang; X. Zhang: Supports of measure solutions for spatially homogeneous Boltzmann equations. Journal of Statistics Physics 124, no. 2, 485-495(2006).

n A.B. Cruzeiro; X. Zhang: Bismut type formulae for diffusion semigroups on Riemannian manifolds. Potential Analysis 25, no. 2, 121-130(2006).

n X. Zhang: $L^p$-theory of semi-linear SPDEs on general measure spaces and applications. J. Func. Anal. 239, no. 1, 44-75(2006).

n X. Zhang; J. Zhu: Non-Lipschitz stochastic differential equations driven by multi-parameter Brownian motions. Stochastic and Dynamic 6, no. 3, 329-340.

n J. Ren; X. Zhang: Continuity modulus of stochastic homeomorphism flows for SDEs with non-Lipschitz coefficients. J. Func. Anal. 241, 2, Pages 439-456(2006).

n X. Zhang: Homeomorphic flows for multi dimensional SDEs with non-Lipschitz coefficients. Stochastic Process. Appl. 115, 435-448(2005).

n J. Ren; X. Zhang: Schilder theorem for the Brownian motion on the diffeomorphism group of the circle. J. Func. Anal. 224, I. 1, 107-133(2005).

n J. Ren; X. Zhang: Freidlin-Wentzell's large deviations for homeomorphism flows of non-Lipschitz SDEs. Bull. Sci. Math. 2 Serie. 129, 8, 643-655(2005).

n X. Zhang: Strong solutions of SDEs with singular drift and Sobolev diffusion coefficients. Stochastic Process. Appl. 115, 11, 1805-1818(2005).

n N. Privault; X. Zhang: Deviation inequalities and law of iterated logarithm on the path space over loop groups. Stochastic and Stochastic Reports 77, no. 6, 515-536(2005).

n X. Zhang: Horizontal lift of Ornstein-Uhlenbeck process on path space over Riemannian manifold. Bull. Sci. Math. 2 Serie. 128, no. 5, 333-340(2004).

n J. Ren; X. Zhang: Path continuity of fractional Dirichlet functionals. Bull. Sci. Math. 2 Serie. 127, no. 4, 368-378(2003).

n A.B. Cruzeiro; X. Zhang: Finite dimensional approximation of Riemannian path space geometry. J. Func. Anal. 205, no. 1, 206-270(2003).

n X. Zhang: Regularity of stopping times of diffusion processes in Besov spaces. Studia Mathematica 151, no. 1, 23-29(2002).

n J. Ren; X. Zhang: Quasi sure analysis of two parameter stochastic differential equation. Stochastics and Stochastics Reports 72, no. 3-4, 251-276(2002).

n H. Airault, J. Ren and X. Zhang: Smoothness of local times of semimartingales. C. R. Acad. Sci. Paris, Serie 1. 330, no. 8, 719-724(2000).

n H. Airault; X. Zhang: Smoothness of indicator functions of some sets in Wiener spaces. J. Math. Pures Appl. 79, no. 5, 515-523(2000).


Editorial Board Service

2017--present, Potential Analysis, Editorial board

2017--present, Statistics & Probability Letters, Associate Editor

2021--present, Communications in Mathematics and Statistics, Editor board

2021--present, Communications on Pure and Applied Analysis, Editorial board


Conference Organization

The 42nd conference on Stochastic Processes and their Applications, Wuhan, June 27-July 1, 2022. http://spa2022.whu.edu.cn/index.htm

The 13th Workshop on Markov Processes and Related Topics, Wuhan, July 17-21, 2017.

International Conference on Stochastic Analysis and Related Topics, Wuhan, August 2-6, 2015.


Fundings

01/2018--12/2022, National Natural Science Foundation of China (NSFC) (Grant No. 11731009), Principal Investigator, (重点项目)

01/2014--12/2017, National Natural Science Foundation of China (NSFC) (Grant No. 11325105), Principal Investigator, (杰出青年项目)

01/2013--12/2016, National Natural Science Foundation of China (NSFC) (Grant No. 11271294), Principal Investigator, (面上项目)

01/2010--12/2012, National Natural Science Foundation of China (NSFC) (Grant No. 10971076), Principal Investigator, (面上项目)


Interests

Stochastic (Partial) Differential Equations, Malliavin Calculus, Levy Processes and Nonlocal Operators, Heat Kernel Estimates, Kinetic Equations.