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Graduate Texts in Mathematics
cover

Random Walk, Brownian Motion, and Martingales

Authors: Bhattacharya, Rabi, Waymire, Edward C.

  • 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
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eBook 53,49 €
price for China (P.R.) (gross)
  • The eBook version of this title will be available soon
  • Due: 2021年9月3日
  • ISBN 978-3-030-78939-8
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover 64,99 €
price for China (P.R.) (gross)
  • Due: 2021年9月3日
  • ISBN 978-3-030-78937-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
About this Textbook

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 theory throughout.

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.

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.

Buy this book

eBook 53,49 €
price for China (P.R.) (gross)
  • The eBook version of this title will be available soon
  • Due: 2021年9月3日
  • ISBN 978-3-030-78939-8
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover 64,99 €
price for China (P.R.) (gross)
  • Due: 2021年9月3日
  • ISBN 978-3-030-78937-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
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Bibliographic Information

Bibliographic Information
Book Title
Random Walk, Brownian Motion, and Martingales
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
292
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-78939-8
DOI
10.1007/978-3-030-78939-8
Hardcover ISBN
978-3-030-78937-4
Series ISSN
0072-5285
Edition Number
1
Number of Pages
VIII, 414
Number of Illustrations
20 b/w illustrations
Topics