Title

Rates of convergence in the central limit theorem for Markov chains

Date of Completion

January 2008

Keywords

Mathematics|Statistics

Degree

Ph.D.

Abstract

We consider symmetric Markov chains on the integer lattice that possibly have arbitrarily large jumps. In the literature, it is proven that under certain conditions, a central limit theorem for a sequence of normalized symmetric Markov chains can be established. In this thesis we calculate an (almost polynomial) rate of convergence through techniques that give bounds on the difference of semigroups. ^ In the second part of the thesis, we establish the derivative concept for a large class of stochastic flows. We prove that, under certain differentiability conditions on the integrands in a stochastic differential equation, the derivatives of these processes have a version that is continuous from the right and with limits from the left and are continuous in space, and have moments of all orders. A Taylor expansion is derived as well. ^