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:

When is the ConwayMaxwellPoisson distribution infinitely divisible? (with A. Xia), preprint, 2020.

SL_2(R)developments and signature asymptotics for planar paths with bounded variation (with H. Boedihardjo), preprint, 2020.

Lipschitzstability of controlled rough paths and rough differential equations (with H. Boedihardjo), preprint, 2020.

Precise local estimates for differential equations driven by fractional Brownian motion: hypoelliptic case (with C. Ouyang and S. Tindel), preprint, 2020.

Precise local estimates for differential equations driven by fractional Brownian motion: elliptic case (with C. Ouyang and S. Tindel), preprint, 2020.

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

Tail asymptotics of the Brownian signature (with H. Boedihardjo), Trans. Amer. Math. Soc. 372: 585614, 2019.

A nonvanishing property for the signature of a path (with H. Boedihardjo), C. R. Math. Acad. Sci. Paris 357 (2): 120129, 2019.

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

Long time asymptotics of heat kernels and Brownian winding numbers on manifolds with boundary (with G. Iyer), preprint, 2018.

Reconstruction for the signature of a rough path, Proc. Lond. Math. Soc. 114 (3): 495526, 2017.

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

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

On an inversion theorem for Stratonovich's signatures of multidimensional diffusion paths (with Z. Qian), Ann. Inst. Henri Poincaré Probab. Stat. 52 (1): 429447, 2016.

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

The uniqueness of signature problem in the nonMarkov setting (with H. Boedihardjo), Stochastic Process. Appl. 125 (12): 46744701, 2015.

Simple piecewise geodesic interpolation of simple and Jordan curves with applications (with H. Boedihardjo), Constr. Approx. 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.