A technique for exponential change of measure for Markov processes
type: Item
instance of: scholarly article
title: A technique for exponential change of measure for Markov processes
zbMATH Open document ID: 1011.60054
author: Zbigniew Palmowski
author: Tomasz Rolski
published in: Bernoulli
publication date: 2003-05-25T00:00:00Z
review text: This paper presents a detailed account of the change of probability measure technique for càdlàg Markov processes. Consider a Markov process \(X(t)\) on a filtered probability space \((\Omega, {\mathcal F}, \{ {\mathcal F}_t \}, P)\) having extended generator \({\mathbf A}\) with domain \({\mathcal D}({\mathbf A}).\) Let \(\tilde{P}\) be a probability measure on \((\Omega, {\mathcal F})\) such that the procees \(d\tilde{P}_t/dP_t = E^h (t)\) is an exponential martingale, \(h\) is a positive function from \({\mathcal D}({\mathbf A}).\) It is shown that the process \(X(t)\) is a Markov process on the probability space \((\Omega, {\mathcal F}, \{ {\mathcal F}_t \}, \tilde{P}).\) Its extended generator \(\tilde{\mathbf A}\) and sufficient conditions under which \({\mathcal D}(\tilde{\mathbf A}) = {\mathcal D}({\mathbf A})\) are found. The authors also accomodate some non-Markovian processes that are Markovian with a supplementary component, for example, piecewise deterministic Markov processes or Markov additive processes. For diffusion processes, a special case of the theory presented is a Girsanov-type theorem.
reviewed by: Vyacheslav A. Vasiliev
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60J99
zbMATH DE Number: 1877110
zbMATH Keywords: exponential change of measure
zbMATH Keywords: extended generator
zbMATH Keywords: diffusion process
zbMATH Keywords: Markov process
zbMATH Keywords: piecewise deterministic Markov process
zbMATH Keywords: Cameron-Martin-Girsanov theorem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1877110