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. ^
Recommended Citation
Corluy, Marc, "Rates of convergence in the central limit theorem for Markov chains" (2008). Doctoral Dissertations. AAI3340450.
https://digitalcommons.lib.uconn.edu/dissertations/AAI3340450
