Stochastic Analysis of Biochemical Systems

ISBN-13: 9783319168944 / Angielski / Miękka / 2015 / 84 str.

Anderson; David F. Anderson; Thomas Kurtz

Opis

This book focuses on counting processes and continuous-time Markov chains motivated by examples and applications drawn from chemical networks in systems biology. The book should serve well as a supplement for courses in probability and stochastic processes. While the material is presented in a manner most suitable for students who have studied stochastic processes up to and including martingales in continuous time, much of the necessary background material is summarized in the Appendix. Studentsand Researcherswith a solid understanding of calculus, differential equations and elementary probability and whoarewell-motivated by the applications will find this book of interest.David F. Anderson is Associate Professor in the Department of Mathematics at the University of Wisconsin and Thomas G. Kurtz is Emeritus Professor in the Departments of Mathematics and Statistics at that university. Their research is focused on probability and stochastic processes with applications in biology and other areas of science and technology.These notes are based in part on lectures given by Professor Anderson at the University of Wisconsin Madison and by Professor Kurtz at Goethe University Frankfurt."

Recenzje

"For the reader's convenience, the book contains an appendix summarizing the necessary backgrounds on probability theory and stochastic processes. The authors manage to present the materials with clarity, brevity and style. In particular, the carefully chosen examples on the one hand help to illustrate the insights and results, and on the other hand make the book more readable. ... The book provides nice supplementary material for courses in probability and stochastic processes." (Chao Zhu, Mathematical Reviews, March, 2016)

Spis treści

​Infinitesimal specification of continuous time Markov chains.- Models of biochemical reaction systems.-Stationary distributions of stochastically modeled reaction systems.- Analytic approaches to model simplification and approximation.-Numerical methods.-Notes on probability theory and stochastic processes.

O autorze

David F. Anderson and Thomas G. Kurtz are Professors in the Department of Mathematics and Statistics at the University of Wisconsin Madison.