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010   $a3-319-61295-6
024 7 $a10.1007/978-3-319-61295-9
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035   $a(DE-He213)978-3-319-61295-9
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035   $a(PPN)203669959
035   $a(EXLCZ)994340000000062062
100   $a20170720d2017      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aPiecewise deterministic processes in biological models /$fby Ryszard Rudnicki, Marta Tyran-Kami?ska
205   $a1st ed. 2017.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017.
215   $a1 online resource (IX, 169 p. 10 illus.)
225 1 $aSpringerBriefs in Mathematical Methods,$x2365-0826
311 08$a3-319-61293-X 
320   $aIncludes bibliographical references and index.
327   $a1 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.
330   $aThis book presents a concise introduction to piecewise deterministic Markov processes (PDMPs), with particular emphasis on their applications to biological models. Further, it presents examples of biological phenomena, such as gene activity and population growth, where different types of PDMPs appear: continuous time Markov chains, deterministic processes with jumps, processes with switching dynamics, and point processes. Subsequent chapters present the necessary tools from the theory of stochastic processes and semigroups of linear operators, as well as theoretical results concerning the long-time behaviour of stochastic semigroups induced by PDMPs and their applications to biological models.  As such, the book offers a valuable resource for mathematicians and biologists alike. The first group will find new biological models that lead to interesting and often new mathematical questions, while the second can observe how to include seemingly disparate biological proc esses into a unified mathematical theory, and to arrive at revealing biological conclusions.  The target audience primarily comprises of researchers in these two fields, but the book will also benefit graduate students.
410  0$aSpringerBriefs in Mathematical Methods,$x2365-0826
606   $aBiomathematics
606   $aSystems biology
606   $aStatistical physics
606   $aDynamics
606   $aProbabilities
606   $aBiomedical engineering
606   $aGenetics and Population Dynamics$3https://scigraph.springernature.com/ontologies/product-market-codes/M31010
606   $aSystems Biology$3https://scigraph.springernature.com/ontologies/product-market-codes/L15010
606   $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aBiomedical Engineering and Bioengineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T2700X
606   $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090
615  0$aBiomathematics.
615  0$aSystems biology.
615  0$aStatistical physics.
615  0$aDynamics.
615  0$aProbabilities.
615  0$aBiomedical engineering.
615 14$aGenetics and Population Dynamics.
615 24$aSystems Biology.
615 24$aComplex Systems.
615 24$aProbability Theory and Stochastic Processes.
615 24$aBiomedical Engineering and Bioengineering.
615 24$aStatistical Physics and Dynamical Systems.
676   $a519.233
700   $aRudnicki$b Ryszard$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767382
702   $aTyran-Kamin?ska$b Marta$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910254276803321
996   $aPiecewise Deterministic Processes in Biological Models$92108119
997   $aUNINA