Research Papers
Surveys, announcements, and Expository Articles
Editorial Volumes
Book Reviews
Useful Links


Research Papers

[45] A generalized Bismut's formula and applications
     (with Marc Arnaudon, Zhongmin Qian, and Anton Thalmaier), manuscript in preparation. 

[44] Differentiability of reflecting Brownian motion,
     preprint (2009).

[43] Volume Growth and Escape Rate of Brownian Motion on a Complete Riemannian Manifold
     (with Guangnan Qin), to appear in Annals of Probability (2009).

[42] Maximal coupling of Euclidean Brownian motions (with Theodor Sturm),
     preprint, revised (2009).

[41] Asymptotics of implied volatility in local volatility models (with Jim Gatheral,
     Peter Laurence, Cheng Ouyang, and Tai-Ho Wang), preprint, submitted (2009).

[40] Cameron-Martin theorem for complete Riemannian manifolds
     (with Cheng Ouyang), J. Func. Anal., 257, no. 5 (2009).

[39] Volume growth and escape rate of Brownian motion on a Cartan-Hadamard manifold
     (with A. Grigorian), Sobolev Spaces in Mathematics II: Applications in Analysis and Partial
     Differential Equations
, edited by V. Maz'ya, Springer (2008).

[38] Quasi-invariance of the Wiener measure on loop spaces
     (with Fuzhong Gong), to appear in Journal of Theoretical Probability (2009).

[37] Heat equations on manifolds and Bismut's formula,
     Stochastic Analysis and Partial Differential Equations, Contemporary Mathematics, 429 (2007), 121--130.

[36] Characterization of diffusion measures through integration by parts,
     Stein's Method and Applications, edited by A. D. Barbour and Louis H. Y. Cheng, World
     Scientific, Singapore (2005), 195--208.

[35] Brownian motion and the asymptotic Dirichlet problem on a Cartan-Hadamard manifold,
     Annals of Probability, 31, no. 3 (2003), 1305--1319.

[34] Multiplicative functional for the heat equation on manifolds with boundary,
     Michigan Journal of Mathematics, 50 (2002), 351--367.

[33] Quasi-invariance of the Wiener measure on path spaces: noncompact case,
     Journal of Functional Analysis, 193 (2002), 278--290.

[32] Pathwise uniqueness for reflecting Brownian motion in Euclidean domains,
     (with Richard Bass), Probability Theory and Related Fields, 117 (2000), 183-200.

[31] Estimates of derivative of the heat kernel on compact Riemannian manifolds,
     Proceedings of AMS}, 127 (1999), 3739-3744.

[30] Gradient estimates for harmonic functions on manifolds with Lipschitz metrics
     (with Jingyi Chen), Canadian Journal of Mathematics, no. 6 (1998), 1163--1175.

[29] Martingale representation and logarithmic Sobolev inequality,
     (with M. Capitaine and M. Ledoux), Electronic Communications in Probability, 2(1997), 71--81.

[28] Stochastic local Gauss-Bonnet-Chern theorem,
     Journal of Theoretical Probability, 10, no. 4 (1997), 819--834.

[27] Logarithmic Sobolev inequalites on path spaces over compact Riemannian manifolds,
     Communications on Mathematical Physics, 189 (1997), 9--16.

[26] Integration by parts in loop spaces,
     Mathematische Annalen, 309 (1997), 331--339.

[25] Quasi-invariance of the Wiener measure and integration by parts in path spaces,
     Journal of Functional Analysis, 134, no. 2 (1995), 417--450.

[24] Flow and quasi-invariance of the Wiener measure on path spaces,
     Symposia on Pure Mathematics, 57, edited by M. Cranston and M. Pinsky (1995), 265--279.

[23] On the principle of not feeling the boundary,
     Journal of London Mathematical Society, Series 2, 51 (1994), 373--384.

[22] A domain monotonicity property of the Neumann heat kernel,
     Osaka Mathematics Journal
, 31 (1994), 215--233.

[21] Limiting angles of certain two-dimensional Riemannian Brownian Motion,
     (with ilfrid Kendall), Annales de Universit
é de Toulouse, Faculté de Sciences
ematiques, 1, no. 2 (1992), 169--186.

[20] On a class of singular continuous distribution functions,
     Elemente der Mathematik, 47 (1992), 169--172.

[19] On the Θ-function of a Riemannian manifold with boundary,
     Transactions of the AMS, 333, no. 2 (1992), 643--671.

[18] Some potential theory of reflecting Brownian motion in Hölder and Lipschitz domains
     (with Rich Bass),
     Annals of Probability, 19, no. 2 (1991), 486--508.

[17] The semimartingale structure of reflecting Brownian motion (with Rich Bass),
     Proc. of Amer. Math. Soc., 104, no. 4 (1990), 1007--1010.

[16] Heat kernel on non-complete manifolds,
     Indiana Math. J., 39, no.2 (199), 431--442.

[15] Brownian bridges on complete Riemannian manifolds,
     Probability Theory and Related Fields, 84 (1990), 103--118.

[14] Asymptotic behavior of solutions of oblique derivative boundary value problem,
     Michigan Math. J., 36 (1989), 221--244.

[13] Heat diffusion semigroup on complete Riemannian manifolds,
     Annals of Prob., 17, no. 3 (1989), 1248--1254.

[12] Smoothness of Convex hull of planar Brownian motion (with Mike Cranston and Peter March),
     Annals of Prob., 17 (1989), 144--150.

[11] Brownian motion and Riemannian geometry,
     Geometry of Random Motion, edited by R. Durrett and M. Pinsky, Contemporary Math.,
     American Mathematical Society, 73 (1987), 95--104.

[10] Short-time asymptotics of the heat kernel on concave boundary,
     SIAM J. of Math. Analysis, 20, no. 5 (1989), 1109--1127.

[9] Brownian excursions from extremal processes,
    (with Peter March), Sem. des Prob., XXII, Lecture Notes in Math., Birkhauser, 1321 (1988), 502--507.

[8] On the Poisson kernel of Neumann problem of Schrödinger operators,
    J. London Math. Soc., 12 (1987), 370-384.

[7] Branching Brownian motion and Dirichlet boundary value problem of a nonlinear equation,
    Seminar on Stochastic Processes, Birkhauser (1986), 71-83 (1986).

[6] On excursions of reflecting Brownian Motion,
    Trans. Amer. Math. Soc., 298 (1986), 239-264.

[5] Limiting angle of certain Riemannian Brownian motions (with Peter March),
    Comm. Pure Appl. Math. 23 (1985), 768--775.

[4] Brownian exit distribution of a ball,
    Seminar on Stochastic Processes, Birkhauser (1985), 108-116.

[3] Probabilistic approach to the Neumann problem,
    Comm. Pure Appl. Math., 23 (1985), 445-475.

[2] Gauge theory of the Neumann problem (with K.L. Chung),
    Seminar on Stochastic Processes, Birkhauser (1984), 63-70.

[1] A note on the logarithmic potential (关于对数位势的一个注记),
    J. of Math. Research and Expositions, 3(1982), 83-88.

Surveys, announcements, and Expository Articles

[6] Quasi-invariance of the Wiener measure on the loop space over a Riemannian manifold,

    in Heat Kernel, Stochastic Processes, and Functional Inequalities,

    Mathematische Forschungsinstitut Oberwolfach Report 54 (2005), 32-34.


[5] Analysis on path and loop spaces,

    Probability Theory and Applications, IAS/Park City Mathematics Series,

    Volume 6, edited by Elton P. Hsu and S. R. S. Varadhan, American

    Mathematical Society/Institute for Advanced Study (80 pages) (1999).

[4] Analysis in path and loop spaces,

    New Trends in Stochastic Analysis, edited by K. D. Elworthy, Shigeo
    Kusuoka, and Ichiro Shigekawa, World Scientific, Singapore (1997), 168--181.

[3] Inégalité logarithmique de Sobolev sur l'espace d'une variété riemannienne,

    Comptes Rendues de l'Academie des

    Sciences, 320, Série I (1994), 1009-1012.


[2] Sur la Θ-fonction d'une variété riemannienne á bord,

    Compte Rendu de l'Academie des Sciences, 309,

    Série I (1989), 507-510.


[1] Probabilistic methods in differential geometry,

    Seminar on Stochastic Processes, edited by E. Cinlar et al.,

    Birkhauser, Boston (1990), 123-134.





[1] Stochastic Analysis on Manifolds (AMS Graduate Series in Mathematics, Volume 38, 2002)

Editorial Volumes

[3] Selected Works of Kai Lai Chung, World Scientific (2009)

[2] Stochastic Analysis and Partial Differential Equations, AMS Contemporary Mathematics, VoLume 429 (2007)

[1] Probability Theory and Applications (with S. R. S. Varadhan), AMS IAS/Park City Mathematics Series, Volume 6 (1999)

Book Reviews

[2] Review of Daniel W. Stroock's An Introduction to the Analysis of Paths on a Riemannian manifold,
    Mathematical Reviews

[1] Book review of Richard F. Bass's Probabilistic Techniques in Analysis,
    Annals of Probability, 26, no.3 (1998), 1403-- 1405.

Useful Links

    Midwest Probability Colloquium (31st Meeting, 2009)