Palmowski, Zbigniew; Rolski, Tomasz A technique for exponential change of measure for Markov processes. (English) Zbl 1011.60054 Bernoulli 8, No. 6, 767-785 (2002). 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. Reviewer: Vjatscheslav Vasiliev (Tomsk) Cited in 3 ReviewsCited in 53 Documents MSC: 60J25 Continuous-time Markov processes on general state spaces 60J60 Diffusion processes 60G44 Martingales with continuous parameter 60G57 Random measures 60J99 Markov processes Keywords:exponential change of measure; extended generator; diffusion process; Markov process; piecewise deterministic Markov process; Cameron-Martin-Girsanov theorem × Cite Format Result Cite Review PDF