Graduate Texts in Mathematics
cover

Random Walk, Brownian Motion, and Martingales

Autoren: 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
Weitere Vorteile

Dieses Buch kaufen

eBook 53,49 €
Preis für Deutschland (Brutto)
  • Die eBook-Version des Titels ist in Kürze verfügbar
  • Erscheinungstermin: 18. September 2021
  • ISBN 978-3-030-78939-8
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate:
  • eBooks sind auf allen Endgeräten nutzbar
Hardcover 69,54 €
Preis für Deutschland (Brutto)
Über dieses Lehrbuch

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.

Über die Autor*innen

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.

Dieses Buch kaufen

eBook 53,49 €
Preis für Deutschland (Brutto)
  • Die eBook-Version des Titels ist in Kürze verfügbar
  • Erscheinungstermin: 18. September 2021
  • ISBN 978-3-030-78939-8
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate:
  • eBooks sind auf allen Endgeräten nutzbar
Hardcover 69,54 €
Preis für Deutschland (Brutto)
Loading...

Services zu diesem Buch

Bibliografische Information

Bibliographic Information
Buchtitel
Random Walk, Brownian Motion, and Martingales
Autoren
Titel der Buchreihe
Graduate Texts in Mathematics
Buchreihen Band
292
Copyright
2021
Verlag
Springer International Publishing
Copyright Inhaber
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
Buchreihen ISSN
0072-5285
Auflage
1
Seitenzahl
XIII, 400
Anzahl der Bilder
20 schwarz-weiß Abbildungen
Themen