Functional CLT and Berry-Esseen estimates for non-homogeneous random walks.

Abstract

In this thesis, we establish a Trotter-Kato type theorem. More precisely, we charac- terize the convergence in distribution of Feller processes by examining the convergence of their generators. The main contribution here is to obtain quantitative rate estimates in the vague topology for fixed times. As an important application, a central functional limit theorem is derived for random walks on the positive half-line, which converges to Brownian motions on the positive half-line with boundary conditions, as well as random walks on the line converging to the Snapping Out Brownian motion.