Classical and Spatial Stochastic Processes: With Applications to Biology

✍ Scribed by Rinaldo B. Schinazi (auth.)

• Publisher: Birkhäuser
• Year: 2014
• Tongue: English
• Leaves: 268
• Edition: 2
• Category: Library

✦ Synopsis

The revised and expanded edition of this textbook presents the concepts and applications of random processes with the same illuminating simplicity as its first edition, but with the notable addition of substantial modern material on biological modeling. While still treating many important problems in fields such as engineering and mathematical physics, the book also focuses on the highly relevant topics of cancerous mutations, influenza evolution, drug resistance, and immune response. The models used elegantly apply various classical stochastic models presented earlier in the text, and exercises are included throughout to reinforce essential concepts.

The second edition of Classical and Spatial Stochastic Processes is suitable as a textbook for courses in stochastic processes at the advanced-undergraduate and graduate levels, or as a self-study resource for researchers and practitioners in mathematics, engineering, physics, and mathematical biology.

Reviews of the first edition:

An appetizing textbook for a first course in stochastic processes. It guides the reader in a very clever manner from classical ideas to some of the most interesting modern results. … All essential facts are presented with clear proofs, illustrated by beautiful examples. … The book is well organized, has informative chapter summaries, and presents interesting exercises. The clear proofs are concentrated at the ends of the chapters making it easy to find the results. The style is a good balance of mathematical rigorosity and user-friendly explanation. —Biometric Journal

This small book is well-written and well-organized. ... Only simple results are treated ... but at the same time many ideas needed for more complicated cases are hidden and in fact very close. The second part is a really elementary introduction to the area of spatial processes. ... All sections are easily readable and it is rather tentative for the reviewer to learn them more deeply by organizing a course based on this book. The reader can be really surprised seeing how simple the lectures on these complicated topics can be. At the same time such important questions as phase transitions and their properties for some models and the estimates for certain critical values are discussed rigorously. ... This is indeed a first course on stochastic processes and also a masterful introduction to some modern chapters of the theory. —Zentralblatt Math

✦ Table of Contents

Front Matter....Pages i-xii
A Short Probability Review....Pages 1-15
Discrete Time Branching Process....Pages 17-46
The Simple Symmetric Random Walk....Pages 47-65
Asymmetric and Higher Dimension Random Walks....Pages 67-80
Discrete Time Markov Chains....Pages 81-103
Stationary Distributions for Discrete Time Markov Chains....Pages 105-129
The Poisson Process....Pages 131-149
Continuous Time Branching Processes....Pages 151-173
Continuous Time Birth and Death Chains....Pages 175-195
Percolation....Pages 197-218
A Cellular Automaton....Pages 219-229
A Branching Random Walk....Pages 231-249
The Contact Process on a Homogeneous Tree....Pages 251-256
Back Matter....Pages 257-268

✦ Subjects

Applications of Mathematics