Stochastic Analysis of Biochemical Systems

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. Students and Researchers with a solid understanding of calculus, differential equations and elementary probability and who are well-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. 

• Continuous time Markov chains
• Langevin approximation
• Models of biochemical systems
• Reaction network
• Stationary distributions
• central limit theorem
• diffusion approximation
• law of large numbers
• law of mass action
• systems biology

“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)

• Department of Mathematics, University of Wisconsin, Madison, Madison, USA

  David F. Anderson

• Departments of Mathematics and Statistics, University of Wisconsin, Madison, USA

  Thomas G. Kurtz

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