Piecewise Deterministic Processes in Biological Models. 1st ed. 2017

種類:

電子ブック

責任表示:

by Ryszard Rudnicki, Marta Tyran-Kamińska

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Rudnicki, Ryszard.
• Tyran-Kamińska, Marta.
• SpringerLink (Online service)

シリーズ名:

SpringerBriefs in Mathematical Methods ;

ISBN:

9783319612959 [3319612956]    

注記:

1 Biological Models -- 2 Markov Processes -- 3 Operator Semigroups -- 4 Stochastic Semigroups -- 5 Asymptotic Properties of Stochastic Semigroups — General Results -- 6 Asymptotic Properties of Stochastic Semigroups — Applications.
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 proc esses into a unified mathematical theory, a

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