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Research Interests:

• Rough paths, the signature transform
• Stochastic/Rough differential equations, diffusion processes
• Gaussian processes, the Malliavin calculus
• Stochastic analysis on manifolds

Preprints and publications:

• A coupling between random walks in random environments and Brox's diffusion(with M. Gradinaru and S. Tindel), arXiv preprint, 2024.
• Stochastic domination of exit times for random walks and Brownian motion with drift(with Gregory Markowsky), arXiv preprint, 2024.
• 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.
• Non-degeneracy of stochastic line integrals (with S. Wang), Electronic Journal of Probability 28: 1-28, 2023.
• When is the Conway-Maxwell-Poisson 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 Probability 50 (2): 649-687, 2022. The original version of this article can be found here.
• Lipschitz-stability of controlled rough paths and rough differential equations (with H. Boedihardjo), Osaka Journal of Mathematics 59 (3): 653-682, 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: 1297-1323, 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: 585-614, 2019.
• A non-vanishing property for the signature of a path (with H. Boedihardjo), Comptes Rendus Mathematique 357 (2): 120-129, 2019.
• A quasi-sure non-degeneracy property for the Brownian rough path (with H. Boedihardjo, X. Liu and Z. Qian), Potential Analysis 51 (1): 1-21, 2019.
• Reconstruction for the signature of a rough path, Proceedings of the London Mathematical Society 114 (3): 495-526, 2017.
• Finite dimensional characteristic functions of the Brownian rough path (with Z. Qian), Frontier of Mathematics in China 12 (4): 859-877, 2017.
• The signature of a rough path: uniqueness (with H. Boedihardjo, T. Lyons and D. Yang), Advances in Mathematics 293: 720-737, 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): 429-447, 2016.
• Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities (with H. Boedihardjo and Z. Qian), Osaka Journal of Mathematics 53 (4): 941-970, 2016.
• The uniqueness of signature problem in the non-Markov setting (with H. Boedihardjo), Stochastic Processes and Their Applications 125 (12): 4674-4701, 2015.
• Simple piecewise geodesic interpolation of simple and Jordan curves with applications (with H. Boedihardjo), Constructive Approximation 42 (1): 161-180, 2015.
• G-Brownian motion as rough paths and differential equations driven by G-Brownian motion (with Z. Qian and D. Yang), Séminaire de Probabilités XLVI, Lecture Notes in Mathematics, 125-193, 2014.