Piecewise Deterministic Processes in Biological Models

1. Auflage 2017
ISBN: 978-3-319-61293-5
Verlag: Springer

Buch, Englisch, 169 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 2818 g

Reihe: SpringerBriefs in Mathematical Methods

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

essesinto 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.

Zielgruppe

Research

Autoren/Hrsg.

Rudnicki, Ryszard

Tyran-Kaminska, Marta

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Medizintechnik, Biomedizintechnik
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizin, Gesundheitswesen Medizintechnik, Biomedizintechnik, Medizinische Werkstoffe
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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.