A first look at stochastic processes [electronic resource] / Jeffrey S. Rosenthal.
By: Rosenthal, Jeffrey S
.
Material type: 
BookPublisher: Singapore : World Scientific Publishing Co. Pte Ltd., 2019, ©2020Description: 1 online resource (212 p.) : ill.ISBN: 9789811207914.Subject(s): Stochastic processes | Stochastic processes -- Mathematical models | Electronic booksDDC classification: 519.2 Online resources: Access to full text is restricted to subscribers. Summary: "This textbook introduces the theory of stochastic processes, that is, randomness which proceeds in time. Using concrete examples like repeated gambling and jumping frogs, it presents fundamental mathematical results through simple, clear, logical theorems and examples. It covers in detail such essential material as Markov chain recurrence criteria, the Markov chain convergence theorem, and optional stopping theorems for martingales. The final chapter provides a brief introduction to Brownian motion, Markov processes in continuous time and space, Poisson processes, and renewal theory. Interspersed throughout are applications to such topics as gambler's ruin probabilities, random walks on graphs, sequence waiting times, branching processes, stock option pricing, and Markov Chain Monte Carlo (MCMC) algorithms. The focus is always on making the theory as well-motivated and accessible as possible, to allow students and readers to learn this fascinating subject as easily and painlessly as possible."-- Publisher's website.
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Online resource; title from title screen (World Scientific, viewed October 25, 2019).
Includes bibliographical references and index.
"This textbook introduces the theory of stochastic processes, that is, randomness which proceeds in time. Using concrete examples like repeated gambling and jumping frogs, it presents fundamental mathematical results through simple, clear, logical theorems and examples. It covers in detail such essential material as Markov chain recurrence criteria, the Markov chain convergence theorem, and optional stopping theorems for martingales. The final chapter provides a brief introduction to Brownian motion, Markov processes in continuous time and space, Poisson processes, and renewal theory. Interspersed throughout are applications to such topics as gambler's ruin probabilities, random walks on graphs, sequence waiting times, branching processes, stock option pricing, and Markov Chain Monte Carlo (MCMC) algorithms. The focus is always on making the theory as well-motivated and accessible as possible, to allow students and readers to learn this fascinating subject as easily and painlessly as possible."-- Publisher's website.
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