Large deviations and parameter estimations for small noise diffusion processes

In this thesis, we study large deviations and parameter estimations for small noise diffusion processes. In Chapter 1, we start with the classical limit theorems to intuitively introduce large deviations and parameter estimations, which provide for further developments in the thesis.

The first part, consisting of Chapters 2 - 4, is on large deviations. In Chapter 2, we begin with the simple stochastic differential equation to explain the idea behind the proof of the nonlinear semigroup method, which is used to prove large deviations in Chapters 3 and 4. In the process, viscosity solutions and the Hamilton-Jacobi-Bellman equations are introduced...