Markov Renewal and Piecewise Deterministic Processes

Christiane Cocozza-Thivent was trained in probability theory at Laboratoire de Probabilités of Université Pierre et Marie Curie (Paris VI University). In 1983 she defended her State doctorate whose main subject was infinite particle systems.In 1986 she became full professor at Université de Technologie de Compiègne (France) where she supervised theses in image processing, speech recognition and reliability, in partnership with industrial companies. In 1991 she was appointed at Université Paris-Est Marne-la-Vallée (now Gustave Eiffel University) where she initiated and was in charge of the applied mathematics cursus.Her research interests include stochastic models in relation with industrial problems and especially with predictive reliability.

• Tools.- Markov renewal processes and related processes.- First steps with PDMP.- Hitting time distribution.- Intensity of some marked point pocesses.- Generalized Kolmogorov equations.- A martingale approach.- Stability.- Numerical methods.- Switching Processes.- Tools.- Interarrival distribution with several Dirac measures.- Algorithm convergence's proof.

“Reading the book is instructive and enjoyable. The author, with a rich experience in the field, proposes us new perspectives on the Markov processes and their applications.” (Eugen Paltanea, zbMATH 1483.60001, 2022)