Rinaldo B. Schinazi

Classical and Spatial Stochastic Processes (eBook, PDF)

With Applications to Biology

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Nature Switzerland
• Seitenzahl: 286
• Erscheinungstermin: 26. Dezember 2024
• Englisch
• ISBN-13: 9783031777608
• Artikelnr.: 72680600

Autorenporträt

Rinaldo Schinazi is a Professor of Mathematics at the University of Colorado.

Inhaltsangabe

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.

Rezensionen

"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.