Adina Oprisan

Graduation Semester and Year

2009

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Andrzej Korzeniowski

Abstract

We study a family of stochastic additive functionals of Markov processes with locally independent increments switched by jump Markov processes in an asymptotic split phase space. Based on an averaging limit theorem, we obtain a large deviation result for this stochastic evolutionary system using a weak convergence approach. Examples, including compound Poisson processes, illustrate cases in which the rate function is calculated in an explicit form.We prove also a large deviation principle for a class of empirical processes associated with additive functionals of Markov processes that were shown to have a martingale decomposition. Functional almost everywhere central limit theorems are established and the large deviation results are derived.

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Download

Included in

Mathematics Commons

Share

COinS