Overview
- Offers an accessible introduction to the rigorous study of stochastic processes
- Builds from simple examples to formal proofs, illuminating key ideas and computations
- Showcases a selection of important contemporary applications, including mathematical finance, optimal stopping, and ruin theory
Part of the book series: Graduate Texts in Mathematics (GTM, volume 292)
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Table of contents (28 chapters)
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Front Matter
Keywords
- Stochastic processes textbook
- Random walk mathematics
- Branching processes mathematics
- Martingales mathematics
- Brownian motion textbook
- Poisson processes
- Kolmogorov-Chentsov theorem
- Markov property
- strong Markov property
- Simple random walk
- Renewal theory mathematics
- Mathematical finance stochastic processes
- Optimal stopping
- Branching random walk
- Navier-Stokes equations
About this book
This textbook offers an approachable introduction to stochastic processes that explores the four pillars of random walk, branching processes, Brownian motion, and martingales. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study.
Consisting of many short chapters, the book begins with a comprehensive account of the simple random walk in one dimension. From here, different paths may be chosen according to interest. Themes span Poisson processes, branching processes, the Kolmogorov–Chentsov theorem, martingales, renewal theory, and Brownian motion. Special topics follow, showcasing a selection of important contemporary applications, including mathematical finance, optimal stopping, ruin theory, branching random walk, and equations of fluids. Engaging exercises accompany the theorythroughout.
Random Walk, Brownian Motion, and Martingales is an ideal introduction to the rigorous study of stochastic processes. Students and instructors alike will appreciate the accessible, example-driven approach. A single, graduate-level course in probability is assumed.
Reviews
Authors and Affiliations
About the authors
Rabi Bhattacharya is Professor of Mathematics at The University of Arizona. He is a Fellow of the Institute of Mathematical Statistics and a recipient of the U.S. Senior Scientist Humboldt Award and of a Guggenheim Fellowship. He has made significant contributions to the theory and application of Markov processes, and more recently, nonparametric statistical inference on manifolds. He has served on editorial boards of many international journals and has published several research monographs and graduate texts on probability and statistics.
Edward C. Waymire is Emeritus Professor of Mathematics at Oregon State University. He received a PhD in mathematics from the University of Arizona in the theory of interacting particle systems. His primary research concerns applications of probability and stochastic processes to problems of contemporary applied mathematics pertaining to various types of flows, dispersion, and random disorder. He is a former chief editor of the Annals of Applied Probability, and past president of the Bernoulli Society for Mathematical Statistics and Probability.
Both authors have co-authored numerous books, including A Basic Course in Probability Theory, which is an ideal companion to the current volume.
Bibliographic Information
Book Title: Random Walk, Brownian Motion, and Martingales
Authors: Rabi Bhattacharya, Edward C. Waymire
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-030-78939-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-78937-4Published: 21 September 2021
eBook ISBN: 978-3-030-78939-8Published: 20 September 2021
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XV, 396
Number of Illustrations: 20 b/w illustrations
Topics: Probability Theory and Stochastic Processes, Statistics and Computing/Statistics Programs