Probability: Theory and Examples

Durrett, Rick

ISBN 10: 1108473687 / ISBN 13: 9781108473682

Editore: CAMBRIDGE, 2019

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Titolo: Probability: Theory and Examples

Casa editrice: CAMBRIDGE

Data di pubblicazione: 2019

Legatura: Hardcover

Condizione: New

Edizione: quinta edizione o successive

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Riassunto:

This lively introduction to measure-theoretic probability theory covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. Concentrating on results that are the most useful for applications, this comprehensive treatment is a rigorous graduate text and reference. Operating under the philosophy that the best way to learn probability is to see it in action, the book contains extended examples that apply the theory to concrete applications. This fifth edition contains a new chapter on multidimensional Brownian motion and its relationship to partial differential equations (PDEs), an advanced topic that is finding new applications. Setting the foundation for this expansion, Chapter 7 now features a proof of Itô's formula. Key exercises that previously were simply proofs left to the reader have been directly inserted into the text as lemmas. The new edition re-instates discussion about the central limit theorem for martingales and stationary sequences.

Descrizione del libro:

The new edition of this lively but rigorous introduction to measure theoretic probability theory, designed for use in a graduate course, contains a new chapter on multidimensional Brownian motion and its relationship to partial differential equations (PDEs), a topic that is finding new applications. Some 200 examples and 450 exercises help readers build practical intuition.