Rabi Bhattacharya, Edward C. Waymire

Gebundenes Buch

Random Walk, Brownian Motion, and Martingales

Beschreibung

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.

Autor

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.

Produktdetails

• Graduate Texts in Mathematics 292
• Verlag: Springer / Springer International Publishing / Springer, Berlin
• Artikelnr. des Verlages: 978-3-030-78937-4
• 2021
• Seitenzahl: 412
• Erscheinungstermin: 21. September 2021
• Englisch
• Abmessung: 241mm x 160mm x 27mm
• Gewicht: 856g
• ISBN-13: 9783030789374
• ISBN-10: 3030789373
• Artikelnr.: 61845384

Rezensionen

"The present text does an outstanding job of presenting many complementary aspects of the subject in a unified and coherent way ... the subject matter and appreciation for the work of the authors in producing such an engaging and readable book. The authors suggest various models for graduate-level courses ... . There is a great deal in the book that will be interesting, stimulating, and enjoyable for readers with an interest in probability theory and stochiastic processes." (Andrew Wade, zbMATH 1489.60001, 2022)