Abstract
Contrary to the usual practice, martingales are not at the heart of our study of PDMPs, but a book devoted to PDMPs cannot fail to mention those related to them. This chapter contains the classic results on these martingales. It is based on the results mentioned in Appendix A (Sect. A.4) about the compensator of a marked point process and the associated stochastic calculus. The reader who is not specifically interested in martingales can skip this chapter without prejudicing the reading of the following ones.
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Cocozza-Thivent, C. (2021). A Martingale Approach. In: Markov Renewal and Piecewise Deterministic Processes. Probability Theory and Stochastic Modelling, vol 100. Springer, Cham. https://doi.org/10.1007/978-3-030-70447-6_7
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DOI: https://doi.org/10.1007/978-3-030-70447-6_7
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