- 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):
- Stochastic differential equations
- Analysis of rough paths and their signatures
- Gaussian analysis and the Malliavin calculus
- Stochastic analysis on manifolds
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.
- Math 21240: Matrix Algebra with Applications, Spring 2018, Instructor.
Math 21880: Stochastic Calculus, Fall 2017, Instructor.
- Math 21260: Differential Equations, Spring 2017, Instructor.
Math 21880: Stochastic Calculus, Fall 2016, Instructor.
- Martingales Through Measure Theory, Michaelmas 2015, Tutor.
Differentiable Manifolds and De Rham Cohomology, Hilary 2014, Instructor.
- Metric Spaces and Complex Analysis, Michaelmas 2013, Tutor.
- Analysis and Linear Algebra, Trinity 2013, Tutor.
Last Update: May 2019