Piecewise deterministic processes in biological models / by Ryszard Rudnicki, Marta Tyran-Kamińska.

Format:

Book

Author/Creator:

Rudnicki, Ryszard, Author.

Tyran-Kamińska, Marta, Author.

Series:

SpringerBriefs in Mathematical Methods, 2365-0826

Language:

English

Subjects (All):

Biomathematics.

Systems biology.

Statistical physics.

Dynamics.

Probabilities.

Biomedical engineering.

Genetics and Population Dynamics.

Systems Biology.

Complex Systems.

Probability Theory and Stochastic Processes.

Biomedical Engineering and Bioengineering.

Statistical Physics and Dynamical Systems.

Local Subjects:

Genetics and Population Dynamics.

Systems Biology.

Complex Systems.

Probability Theory and Stochastic Processes.

Biomedical Engineering and Bioengineering.

Statistical Physics and Dynamical Systems.

Physical Description:

1 online resource (IX, 169 p. 10 illus.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

Summary:

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, 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.

Contents:

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.

Notes:

Includes bibliographical references and index.

ISBN:

3-319-61295-6