Piecewise Deterministic Processes in Biological Models
Springer International Publishing (Verlag)
978-3-319-61293-5 (ISBN)
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.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.
| Erscheinungsdatum | 04.08.2017 |
|---|---|
| Reihe/Serie | SpringerBriefs in Applied Sciences and Technology | SpringerBriefs in Mathematical Methods |
| Zusatzinfo | IX, 169 p. 10 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 285 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Naturwissenschaften ► Biologie ► Evolution | |
| Naturwissenschaften ► Biologie ► Genetik / Molekularbiologie | |
| Schlagworte | Applied mathematics • biomedical engineering • Complex Systems • Deterministic Processes with Jumps • dynamics & statics • Dynamics & statics • Genetics and Population Dynamics • Kolmogorov equations • Life sciences: general issues • Mathematics • mathematics and statistics • Piecewise Deterministic Markov Processes • probability & statistics • Probability & statistics • Probability theory and stochastic processes • Statistical Physics • Statistical Physics and Dynamical Systems • Stochastic differential equations • stochastics • Stochastic Semigroups • systems biology |
| ISBN-10 | 3-319-61293-X / 331961293X |
| ISBN-13 | 978-3-319-61293-5 / 9783319612935 |
| Zustand | Neuware |
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