Piecewise Deterministic Processes in Biological Models By Prof. Ryszard Rudnicki, Prof. Marta Tyran-Kamińska
English | PDF | 2017 | 177 Pages | ISBN : 331961293X | 4.8 MB
This book presents a concise introduction to piecewise deterministic Markov processes (PDMPs), with particular emphasis on their applications to biological models. Further, it presents examples of biological phenomena, such as gene activity and population growth, where different types of PDMPs appear: continuous time Markov chains, deterministic processes with jumps, processes with switching dynamics, and point processes. Subsequent chapters present the necessary tools from the theory of stochastic processes and semigroups of linear operators, as well as theoretical results concerning the long-time behaviour of stochastic semigroups induced by PDMPs and their applications to biological models.