Weian Zheng


Professor, Mathematics
School of Physical Sciences

PH.D., University of Strasbourg, Strasbourg, 1984

Phone: (949) 824-5379
Fax: (949) 824-7993
Email: wzheng@uci.edu

University of California, Irvine
Department of Mathematics
Rowland Hall 540C
Mail Code: 3875
Irvine, CA 92697
Research Interests
Probability; stochastic processes
URL
Academic Distinctions
Appointments:
2000 - present: Zi-Jiang Distinguished Professor (part-time), East-China Normal University, Shanghai, China.
1998 - present: Professor, Department of Mathematics, UC Irvine.
Appointments
2000 - present: Zi-Jiang Distinguished Professor (part-time), East-China Normal University, Shanghai, China. 1998 - present: Professor, Department of Mathematics, UC Irvine.
Publications
Publications available on MathSciNet

On Monge–Kantorovich problem in the plane, Comptes Rendus Mathematique Volume 348, Issues 5-6, March 2010, Pages 267-271.
 
Stochastic Volatility Model and Technical Analysis of Stock Price", to appear in Acta Mathematica Sinica, English Series.
 
Han, Dong ; Zhang, Xin Sheng ; Zheng, Wei An. Subcritical, critical and supercritical size distributions in random coagulation-fragmentation processes. Acta Math. Sin. (Engl. Ser.) 24 (2008), no. 1, 121--138.
 
Chen, Xinfu ; Chadam, John ; Jiang, Lishang ; Zheng, Weian. Convexity of the exercise boundary of the American put option on a zero dividend asset. Math. Finance 18 (2008), no. 1, 185--197.
 
Liu, Wei ; Huang, Xudong ; Zheng, Weian. Black-Scholes' model and Bollinger bands. Phys. A 371 (2006), no. 2, 565--571.
 
Xu, Zhi Yan ; Zheng, Wei An. Sharp error estimate for maximum likelihood estimator of nonstationary diffusion processes. Acta Math. Sin. (Engl. Ser.) 21 (2005), no. 2, 303--314.
 
Qian, Zhongmin ; Zheng, Weian. A representation formula for transition probability densities of diffusions and applications. Stochastic Process. Appl. 111 (2004), no. 1, 57--76.
 
Qian, Zhongmin ; Russo, Francesco ; Zheng, Weian. Comparison theorem and estimates for transition probability densities of diffusion processes. Probab. Theory Related Fields 127 (2003), no. 3, 388--406.
 
Roman, Luis J. ; Zhang, Xinsheng ; Zheng, Weian. Rate of convergence in homogenization of parabolic PDEs. Math. Phys. Anal. Geom. 6 (2003), no. 2, 113--124.
 
Zhang, T. S. ; Zheng, W. A. SPDEs driven by space-time white noise in high dimensions: absolute continuity of the law and convergence of solutions. Stoch. Stoch. Rep. 75 (2003), no. 3, 103--128.
 
Piatnitski, A. L. ; Zhao, H. Z. ; Zheng, W. A. Solutions to a class of multidimensional SPDEs. Int. Math. J. 3 (2003), no. 7, 755--774.
 
Qian, Zhongmin ; Zheng, Weian. Sharp bounds for transition probability densities of a class of diffusions. C. R. Math. Acad. Sci. Paris 335 (2002), no. 11, 953--957.
 
Zhang, Yinnan ; Zheng, Weian. Discretizing a backward stochastic differential equation. Int. J. Math. Math. Sci. 32 (2002), no. 2, 103--116.
 
Allouba, Hassan ; Zheng, Weian. Brownian-time processes: the PDE connection and the half-derivative generator. Ann. Probab. 29 (2001), no. 4, 1780--1795.
 
Zheng, Weian. Estimation of the phase transition time in the Stefan problem. Stochastic processes, physics and geometry: new interplays, II (Leipzig, 1999), 633--640, CMS Conf. Proc., 29, Amer. Math. Soc., Providence, RI, 2000.
 
Zheng, Weian. Stability of time-dependent diffusion semigroups and kernels. Acta Math. Sin. (Engl. Ser.) 15 (1999), no. 4, 575--586.
 
Chen, Zhen-Qing ; Qian, Zhongmin ; Hu, Yaozhong ; Zheng, Weian. Stability and approximations of symmetric diffusion semigroups and kernels. J. Funct. Anal. 152 (1998), no. 1, 255--280.
 
Stroock, Daniel W. ; Zheng, Weian. Markov chain approximations to symmetric diffusions. Ann. Inst. H. Poincaré Probab. Statist. 33 (1997), no. 5, 619--649.
 
Zheng, Weian. Meyer's topology and Brownian motion in a composite medium. Séminaire de Probabilités, XXX, 108--116, Lecture Notes in Math., 1626, Springer, Berlin, 1996.
 
Zheng, Weian. Large deviation results without continuity hypothesis on the diffusion term. Stochastic analysis and applications (Powys, 1995), 490--502, World Sci. Publ., River Edge, NJ, 1996.
 
Zheng, Weian. A phase transition speed estimate in the Stefan problem. Proc. Roy. Soc. Edinburgh Sect. A 126 (1996), no. 6, 1341--1347.
 
Zheng, Weian. Brownian motion on a Lipschitz Riemannian manifold composed of different materials. Stochastics Stochastics Rep. 54 (1995), no. 1-2, 75--87.
 
Zheng, Wei An. Conditional propagation of chaos and a class of quasilinear PDE's. Ann. Probab. 23 (1995), no. 3, 1389--1413.
 
Zheng, Wei An. Diffusion processes on a Lipschitz Riemannian manifold and their applications. Stochastic analysis (Ithaca, NY, 1993), 373--381, Proc. Sympos. Pure Math., 57, Amer. Math. Soc., Providence, RI, 1995.
 
Liao, M. ; Zheng, W. A. Radial part of Brownian motion on a Riemannian manifold. Ann. Probab. 23 (1995), no. 1, 173--177.
 
Zheng, Wei An. A large deviation result for a class of Dirichlet processes. Probab. Theory Related Fields 101 (1995), no. 2, 237--249.
 
Zheng, Weian. Heat kernel on a Lipschitz manifold composed of two halfspaces with different metrics. Stochastics Stochastics Rep. 47 (1994), no. 3-4, 201--228.
 
Carmona, René A. ; Zheng, Wei An. Reflecting Brownian motions and comparison theorems for Neumann heat kernels. J. Funct. Anal. 123 (1994), no. 1, 109--128.
 
Zheng, Wei An. On symmetric diffusion processes. Probability theory and its applications in China, 329--333, Contemp. Math., 118, Amer. Math. Soc., Providence, RI, 1991.
 
Zheng, Wei An. On interacting Ornstein-Uhlenbeck processes. Diffusion processes and related problems in analysis, Vol. I (Evanston, IL, 1989), 33--52, Progr. Probab., 22, Birkhäuser Boston, Boston, MA, 1990.
 
Lyons, T. J. ; Zheng, W. A. On conditional diffusion processes. Proc. Roy. Soc. Edinburgh Sect. A 115 (1990), no. 3-4, 243--255.
 
Lyons, T. J. ; Zheng, W. A. Diffusion processes with nonsmooth diffusion coefficients and their density functions. Proc. Roy. Soc. Edinburgh Sect. A 115 (1990), no. 3-4, 231--242.
 
Williams, R. J. ; Zheng, W. A. On reflecting Brownian motion---a weak convergence approach. Ann. Inst. H. Poincaré Probab. Statist. 26 (1990), no. 3, 461--488.
 
Lyons, Terence J. ; Zheng, Wei An. A crossing estimate for the canonical process on a Dirichlet space and a tightness result. Colloque Paul Lévy sur les Processus Stochastiques (Palaiseau, 1987). Astérisque No. 157-158 (1988), 249--271.Lyons, Terence J. ; Zheng, Wei An. A crossing estimate for the canonical process on a Dirichlet space and a tightness result. Colloque Paul Lévy sur les Processus Stochastiques (Palaiseau, 1987). Astérisque No. 157-158 (1988), 249--271.
 
Blanchard, Ph. ; Combe, Ph. ; Zheng, W. Mathematical and physical aspects of stochastic mechanics.Lecture Notes in Physics, 281. Springer-Verlag, Berlin, 1987. viii+171 pp. ISBN: 3-540-18036-2
 
Zheng, Wei An. Semimartingale with smooth density---the problem of “nodes”. Stochastic processes---mathematics and physics, II (Bielefeld, 1985), 356--369, Lecture Notes in Math., 1250, Springer, Berlin, 1987.
 
Zheng, W. A. ; Meyer, P.-A. Correction: “Some results in ‘stochastic mechanics’” [in Seminar on Probability, XVIII, 223--244, Lecture Notes in Math., 1059, Springer, Berlin, 1984; (French) Séminaire de Probabilités, XX, 1984/85, 614, Lecture Notes in Math., 1204, Springer, Berlin, 1986.
 
Zheng, W. A. ; Meyer, P.-A. Sur la contruction de certaines diffusions.(French) [On the construction of certain diffusions] éminaire de Probabilités, XX, 1984/85, 334--337, Lecture Notes in Math., 1204, Springer, Berlin, 1986.
 
Blanchard, Ph. ; Zheng, Wei An. Stochastic variational principle and diffusion processes. Stochastic processes in classical and quantum systems (Ascona, 1985), 109--117, Lecture Notes in Phys., 262, Springer, Berlin, 1986.
 
Blanchard, Ph. ; Zheng, Wei An. Pathwise conservation law for stationary diffusion processes. Stochastic processes in classical and quantum systems (Ascona, 1985), 105--108, Lecture Notes in Phys., 262, Springer, Berlin, 1986.
 
Meyer, P.-A. ; Zheng, W. A. Construction de processus de Nelson réversibles.(French) [Construction of reversible Nelson processes] Séminaire de probabilités, XIX, 1983/84, 12--26, Lecture Notes in Math., 1123, Springer, Berlin, 1985.
 
Zheng, W. A. Tightness results for laws of diffusion processes application to stochastic mechanics. Ann. Inst. H. Poincaré Probab. Statist. 21 (1985), no. 2, 103--124.
 
He, Sheng Wu ; Zheng, Wei An. On discrete filtrations. (Chinese) J. East China Norm. Univ. Natur. Sci. Ed. 1984, no. 2, 1--6.
 
Meyer, P.-A. ; Zheng, W. A. Tightness criteria for laws of semimartingales. Ann. Inst. H. Poincaré Probab. Statist. 20 (1984), no. 4, 353--372.
 
Émery, Michel ; Zheng, W. A. Fonctions convexes et semimartingales dans une variété.(French) [Convex functions and semimartingales in a manifold] Seminar on probability, XVIII, 501--518, Lecture Notes in Math., 1059, Springer, Berlin, 1984.
 
Zheng, W. A. ; Meyer, P.-A. Quelques résultats de “mécanique stochastique”. (French) [Some results in “stochastic mechanics”] eminar on probability, XVIII, 223--244, Lecture Notes in Math., 1059, Springer, Berlin, 1984.
 
He, S. W. ; Zheng, W. A. Remarques sur la convergence des martingales dans les variétés.(French) [Remarks on the convergence of martingales in manifolds] Seminar on probability, XVIII, 174--178, Lecture Notes in Math., 1059, Springer, Berlin, 1984.
 
Zheng, Wei An. Une remarque sur une même I. S. calculée dans deux filtrations.(French) [A remark on the same stochastic integration calculated integral two filtrations] Seminar on probability, XVIII, 172--173, Lecture Notes in Math., 1059, Springer, Berlin, 1984.
 
Zheng, Wei An. ; Meyer, P.-A. Integrales stochastiques non monotones.(French) [Nonmonotonic stochastic integrals] Seminar on probability, XVIII, 154--171, Lecture Notes in Math., 1059, Springer, Berlin, 1984.
 
He, S. W. ; Yan, J. A. ; Zheng, W. A. Sur la convergence des semimartingales continues dans $R^n$ et des martingales dans une variété. (French) [On the convergence of continuous semimartingales in $R^n$ and of martingales in a manifold] With a note by M. Emery.Lecture Notes in Math., 986, Seminar on probability, XVII, 179--186, Springer, Berlin, 1983.
 
Zheng, W. A. Sur la convergence des martingales dans une variété riemannienne. (French) [On the convergence of martingales in a Riemannian manifold] Z. Wahrsch. Verw. Gebiete 63 (1983), no. 4, 511--515.
 
Zheng, Wei An. The absolute value of a local martingale. Sci. Sinica Ser. A 25 (1982), no. 6, 561--571.
 
Zheng, Wei An. Semimartingales in predictable random open sets. Seminar on Probability, XVI, pp. 370--379, Lecture Notes in Math., 920, Springer, Berlin-New York, 1982.
 
Zheng, Wei An. ; He, Sheng Wu . On local times of a certain class of semimartingales. (Chinese) Chinese Ann. Math. 2 (1981), no. 3, 359--364.
 
Zheng, Wei An. On the existence of maximum likelihood estimators. (Chinese) Chinese Ann. Math. 1 (1980), no. 2, 317--324.
 
Zheng, Wei An. ; He, Sheng Wu . On local times and trajectories of the continuous local martingales. (Chinese) Chinese Ann. Math. 1 (1980), no. 3-4, 505--510.
 
Zheng, Wei An. A note on the convergence of sequences of conditional expectations of random variables. Z. Wahrsch. Verw. Gebiete 53 (1980), no. 3, 291--292.
Last updated
06/16/2010