Research Interests:
I am a mathematician working in the interplay between probability and analysis. I particularly enjoy and appreciate the deeper intrinsic connections among different mathematical areas.
My research interests are within the scope of stochastic analysis, rough path theory and their applications, including (but not restricted to):
 Rough paths, the signature transform
 Stochastic/Rough differential equations, diffusion processes
 Gaussian processes, the Malliavin calculus
 Stochastic analysis on manifolds
Preprints and publications:

Expected signature on a Riemannian manifold and its geometric implications(with H. Ni and C. Wang), arXiv preprint, 2024.

On the lack of Gaussian tail for rough line integrals along fractional Brownian paths (with H. Boedihardjo), Probability Theory and Related Fields, 2023.

Nondegeneracy of stochastic line integrals (with S. Wang), Electronic Journal of Probability 28: 128, 2023.

When is the ConwayMaxwellPoisson distribution infinitely divisible? (with A. Xia), Statistics and Probability Letters 181, 2022.

Precise local estimates for differential equations driven by fractional Brownian motion: hypoelliptic case (with C. Ouyang and S. Tindel), The Annals of Probabability 50 (2): 649687, 2022. The original version of this article can be found here.

Lipschitzstability of controlled rough paths and rough differential equations (with H. Boedihardjo), Osaka Journal of Mathematics 59 (3): 653682, 2022.

SL_2(R)developments and signature asymptotics for planar paths with bounded variation (with H. Boedihardjo), Revista Matemática Iberoamericana, 2022.

Precise local estimates for differential equations driven by fractional Brownian motion: elliptic case (with C. Ouyang and S. Tindel), Journal of Theoretical Probability, 2022.

Long time asymptotics of heat kernels and Brownian winding numbers on manifolds with boundary (with G. Iyer), Latin American Journal of Probability and Mathematical Statistics 18: 12971323, 2021.

Path developments and tail asymptotics of signature for pure rough paths (with H. Boedihardjo and N. Souris), Advances in Mathematics 364, 2020.

Tail asymptotics of the Brownian signature (with H. Boedihardjo), Transactions of the American Mathematical Society 372: 585614, 2019.

A nonvanishing property for the signature of a path (with H. Boedihardjo), Comptes Rendus Mathematique 357 (2): 120129, 2019.

A quasisure nondegeneracy property for the Brownian rough path (with H. Boedihardjo, X. Liu and Z. Qian), Potential Analysis 51 (1): 121, 2019.

Reconstruction for the signature of a rough path, Proceedings of the London Mathematical Society 114 (3): 495526, 2017.

Finite dimensional characteristic functions of the Brownian rough path (with Z. Qian), Frontier of Mathematics in China 12 (4): 859877, 2017.

The signature of a rough path: uniqueness (with H. Boedihardjo, T. Lyons and D. Yang), Advances in Mathematics 293: 720737, 2016.

On an inversion theorem for Stratonovich's signatures of multidimensional diffusion paths (with Z. Qian), Annales de l'institut Henri Poincare (B) Probability and Statistics 52 (1): 429447, 2016.

Quasisure existence of Gaussian rough paths and large deviation principles for capacities (with H. Boedihardjo and Z. Qian), Osaka Journal of Mathematics 53 (4): 941970, 2016.

The uniqueness of signature problem in the nonMarkov setting (with H. Boedihardjo), Stochastic Processes and Their Applications 125 (12): 46744701, 2015.

Simple piecewise geodesic interpolation of simple and Jordan curves with applications (with H. Boedihardjo), Constructive Approximation 42 (1): 161180, 2015.
 GBrownian motion as rough paths and differential equations driven by GBrownian motion (with Z. Qian and D. Yang), Séminaire de Probabilités XLVI, Lecture Notes in Mathematics, 125193, 2014.