Classical and Spatial Stochastic Processes : With Applications to Biology / by Rinaldo B. Schinazi.

Format:

Book

Author/Creator:

Schinazi, Rinaldo B., Author.

Language:

English

Subjects (All):

Stochastic processes.

Probabilities.

Biomathematics.

Stochastic Processes.

Probability Theory.

Mathematical and Computational Biology.

Local Subjects:

Stochastic Processes.

Probability Theory.

Mathematical and Computational Biology.

Physical Description:

1 online resource (XII, 286 p. 16 illus.)

Edition:

3rd ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024.

Summary:

This textbook provides an accessible approach to concepts and applications of stochastic processes ideal for a wide range of readers. This revised third edition features an intuitive reorganization with concrete topics introduced early on which are then used to demonstrate more abstract concepts in later chapters. The author has kept chapters short and independent from each other, with several of the longer chapters from previous editions now divided into smaller, more manageable parts. These changes build upon previous editions to allow readers even greater flexibility. The applications that are covered feature active areas of research within biological modeling, such as cancerous mutations, influenza evolution, drug resistance, and immune response. Important problems in fields such as engineering and mathematical physics are presented as well. These topics elegantly apply various classical stochastic models and are motivated throughout with many worked out examples. This third edition of Classical and Spatial Stochastic Processes is suitable as a textbook for a first course in stochastic processes at the upper-undergraduate or graduate level. Because of its accessible approach, it may also be used as a self-study resource for researchers and practitioners in mathematics, engineering, physics, and mathematical biology.

Contents:

Finite Markov Chains

Random walks on finite graphs

The first appearance of a pattern

The ruin problem

The Ehrenfest chain

The simple symmetric random walk

Asymmetric and higher dimension random walks

Discrete time birth and death chains

Discrete time branching process

Recurrence on countable spaces

Stationary distributions on countable spaces

The Poisson process

Continuous time birth and death chains

Continuous time branching processes

Percolation

A cellular automaton

A branching random walk

The contact process on a homogeneous tree

Appendix: A little more probability

Bibliography

Index.

ISBN:

9783031777608