Large deviation and moderate deviation theory and their applications:
Large deviations principle (LDP), Moderate deviations principle (MDP) and Center limit theorem (CLT) together give us a whole picture of stochastic limit theorems of family of random variables, random processes and so on. These subjects play very important roles in both theory and applications.
I focus on the LDP and MDP of diffusions, stochastic processes often given by stochastic differential equations, which are mainly motivated from applications, such as in Physics, Statistics, and among others. Recently, motivated from problems in applications, I also consider LDP and MDP for processes involving anticipating integrals.
I am also interested in the application of these theoretical results in other perspectives such as statistics and statistical physics.
Related Publications:
A Class of Systems of Nonlinear Second-Order Stochastic Differential Equations: Averaging and Large Deviations Principles (with G. Yin), submitted. [arXiv]
Exponential tightness of a family of Skorohod integrals, Electronic Communications in Probability, Vol. 27 (2022), paper no. 1, 1-14. [Journal] [arXiv]