Abstracts
This chapter contains the basic theory for piecewise deterministic Markov processes, whether homogeneous or not, based exclusively on the theory of marked point processes from the previous chapters and presented through the device of viewing a PDMP as a process adapted to the filtration generated by an RCM. The strong Markov property is established, various versions of Itô’s formula for PDMPs are given, the socalled full infinitesimal generator for a homogeneous PDMP is discussed, invariant measures are treated, and the chapter concludes with a section on likelihood processes for PDMPs.
At a first reading one may omit Sections 7.5, 7.7, 7.8 and the last part of Section 7.9 (dealing with multiplicative functionals).
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Chapter 7
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(2006). Piecewise Deterministic Markov Processes. In: Point Process Theory and Applications. Probability and its Applications. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4463-6_7
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DOI: https://doi.org/10.1007/0-8176-4463-6_7
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