04404nam 22007335 450 991025427680332120220329234731.03-319-61295-610.1007/978-3-319-61295-9(CKB)4340000000062062(DE-He213)978-3-319-61295-9(MiAaPQ)EBC4921432(PPN)203669959(EXLCZ)99434000000006206220170720d2017 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierPiecewise deterministic processes in biological models /by Ryszard Rudnicki, Marta Tyran-Kamińska1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (IX, 169 p. 10 illus.)SpringerBriefs in Mathematical Methods,2365-08263-319-61293-X Includes bibliographical references and index.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, 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.SpringerBriefs in Mathematical Methods,2365-0826BiomathematicsSystems biologyStatistical physicsDynamical systemsProbabilitiesBiomedical engineeringGenetics and Population Dynamicshttps://scigraph.springernature.com/ontologies/product-market-codes/M31010Systems Biologyhttps://scigraph.springernature.com/ontologies/product-market-codes/L15010Complex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P33000Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Biomedical Engineering and Bioengineeringhttps://scigraph.springernature.com/ontologies/product-market-codes/T2700XStatistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Biomathematics.Systems biology.Statistical physics.Dynamical systems.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.519.233Rudnicki Ryszardauthttp://id.loc.gov/vocabulary/relators/aut767382Tyran-Kamińska Martaauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910254276803321Piecewise Deterministic Processes in Biological Models2108119UNINA