Piecewise Deterministic Processes in Biological Models - Marta Tyran-Kami¿ska

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Résumé :
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 processesinto 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.

Biographie:
Ryszard Rudnicki, born in 1957, holds an M.Sc. in Mathematics (1980), a Ph.D. (1987), and a Habilitation (1993) from the University of Silesia, Katowice, Poland. He was awarded the scientific title of Professor in 2001 by the Institute of Mathematics of the Polish Academy of Sciences (IMPAS). He currently serves as a Full Professor, the Head of the Katowice Branch of IMPAS, and the Vice-Director of the Mathematical Center for Applications in Science and Technology at IMPAS. From 1980 to 2012, he worked in the Department of Mathematics at the University of Silesia, Katowice. His professional interests include biomathematics, dynamical systems, stochastic processes, and differential equations. He has authored 100 scientific papers, most of which focus on the application of mathematics to biological problems. He has also written four books, including the monograph Piecewise Deterministic Processes in Biological Models (Springer, 2017) with M. Tyran-Kami?ska, published in the same series as his proposed book. Several of his papers focus on Individual-Based Models and limit theorems. Rados?aw Wieczorek is an adjunct professor at the Institute of Mathematics, University of Silesia in Katowice. He graduated both mathematics and physics, but chose to work in biomathematics and got his PhD for the research on fragmentation-coagulation models of phytoplankton at the Institute of Mathematics of Polish Academy of Sciences. His research interests focus on individual-based stochastic processes, especially applied to biological phenomena. He has written a number of papers concerning convergence of the individual-based models....

Sommaire:
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.