Large deviations of local times of Levy processes.

Title: Large deviations of local times of Levy processes.
Identifier: AAI9630438
identifier: 9630438
Creator: Blackburn, Robert Arthur.
Contributor: Adviser: Michael B. Marcus
Date: 1996
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: Consider a real valued symmetric Levy process, where the exponent {dollar}\psi{dollar} of the characteristic function defining the process is regularly varying at infinity with index {dollar}1<\beta\leq2.{dollar} Denote the local time of the Levy process by {dollar}L\sbsp{lcub}t{rcub}{lcub}x{rcub}{dollar} and define the maximum local time by {dollar}L\sbsp{lcub}t{rcub}{lcub}*{rcub}={lcub}\rm sup{rcub}\sb{lcub}x\epsilon R{rcub}L\sbsp{lcub}t{rcub}{lcub}x{rcub}.{dollar} Results are given, for fixed t, which show the limiting behavior of log {dollar}P(L\sbsp{lcub}t{rcub}{lcub}0{rcub}\geq y){dollar} and log {dollar}P(L\sbsp{lcub}t{rcub}{lcub}*{rcub}\geq y),{dollar} as y approaches infinity. The estimates are given in terms of {dollar}\psi.{dollar}.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.