- Lecturer in Probability and Stochastic Processes, University of Melbourne, Feb 2019--Present
- Postdoctoral Associate, Carnegie Mellon University, Sep 2016--Jan 2019
- Research Fellow, University of Oxford, Oct 2014--Jul 2016
- Ph.D. Mathematics, University of Oxford, Oct 2011--Jun 2016
Supervisor: Prof. Zhongmin Qian
Thesis: The Signature of a Rough Path: Uniqueness
- B.Sc. Mathematics, Sun Yat-Sen University, China, Sep 2007--June 2011
Broadly speaking, I am working in the interplay between probability and analysis.
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
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: 585-614, 2019.
A non-vanishing property for the signature of a path (with H. Boedihardjo), C. R. Math. Acad. Sci. Paris 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 Anal. 51 (1): 1-21, 2019.
Reconstruction for the signature of a rough path, Proc. Lond. Math. Soc. 114 (3): 495-526, 2017.
Finite dimensional characteristic functions of the Brownian rough path (with Z. Qian), Front. Math. China 12 (4): 859-877, 2017.
The signature of a rough path: uniqueness (with H. Boedihardjo, T. Lyons and D. Yang), Adv. Math. 293: 720-737, 2016.
On an inversion theorem for Stratonovich's signatures of multidimensional diffusion paths (with Z. Qian), Ann. Inst. Henri Poincaré Probab. Stat. 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 J. Math. 53 (4): 941-970, 2016.
The uniqueness of signature problem in the non-Markov setting (with H. Boedihardjo), Stochastic Process. Appl. 125 (12): 4674-4701, 2015.
Simple piecewise geodesic interpolation of simple and Jordan curves with applications (with H. Boedihardjo), Constr. Approx. 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.
MAST90081: Advanced Probability, Semester 1 2020.
- MAST20004: Probability, Semester 2 2019.
- Math 21240: Matrix Algebra with Applications, Spring 2018.
Math 21880: Stochastic Calculus, Fall 2017.
- Math 21260: Differential Equations, Spring 2017.
- Math 21880: Stochastic Calculus, Fall 2016.
- Differentiable Manifolds and De Rham Cohomology, Hilary 2014.
- Associate editor, Stochastic Analysis and Applications, April 2020 -- present.
Last Update: June 2020