Piecewise Deterministic Processes in Biological Models

Description

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. As such, the book offers a valuable resource for mathematicians and biologists alike. The first group will find new biological models that lead to interesting and often new mathematical questions, while the second can observe how to include seemingly disparate biological processes into a unified mathematical theory, and to arrive at revealing biological conclusions. The target audience primarily comprises of researchers in these two fields, but the book will also benefit graduate students. Front Matter....Pages i-ix Biological Models....Pages 1-32 Markov Processes....Pages 33-62 Operator Semigroups....Pages 63-82 Stochastic Semigroups....Pages 83-114 Asymptotic Properties of Stochastic Semigroups—General Results....Pages 115-128 Asymptotic Properties of Stochastic Semigroups—Applications....Pages 129-147 Back Matter....Pages 149-169