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Piecewise deterministic processes in biological models

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 appea...

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Detalles Bibliográficos
Autores principales: Rudnicki, Ryszard, Tyran-Kamińska, Marta
Lenguaje:eng
Publicado: Springer 2017
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-61295-9
http://cds.cern.ch/record/2276953
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author Rudnicki, Ryszard
Tyran-Kamińska, Marta
author_facet Rudnicki, Ryszard
Tyran-Kamińska, Marta
author_sort Rudnicki, Ryszard
collection CERN
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.
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spelling cern-22769532021-04-21T19:08:25Zdoi:10.1007/978-3-319-61295-9http://cds.cern.ch/record/2276953engRudnicki, RyszardTyran-Kamińska, MartaPiecewise deterministic processes in biological modelsMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:22769532017
spellingShingle Mathematical Physics and Mathematics
Rudnicki, Ryszard
Tyran-Kamińska, Marta
Piecewise deterministic processes in biological models
title Piecewise deterministic processes in biological models
title_full Piecewise deterministic processes in biological models
title_fullStr Piecewise deterministic processes in biological models
title_full_unstemmed Piecewise deterministic processes in biological models
title_short Piecewise deterministic processes in biological models
title_sort piecewise deterministic processes in biological models
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-61295-9
http://cds.cern.ch/record/2276953
work_keys_str_mv AT rudnickiryszard piecewisedeterministicprocessesinbiologicalmodels
AT tyrankaminskamarta piecewisedeterministicprocessesinbiologicalmodels