Cited by 858Probability and Statistical ResearchStochastic processes and statistical mechanicsStochastic processes and financial applications

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Probability: Theory and Examples

Durrett, Rick·2019·Cambridge University Press eBooks

DOI 10.1017/9781108591034

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Abstract

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.

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Authors: Durrett, R.
Affiliations: Duke University (US)
Corresponding author: Durrett, Rick
ORCID: Durrett, Rick
Venue: Cambridge University Press eBooks
Publisher: Cambridge University Press
Published: 2019-04-05
DOI: 10.1017/9781108591034
OpenAlex: W4211192810
Cited by: 857
References: 129
Citations by year: 2026: 129 · 2025: 171 · 2024: 141 · 2023: 139 · 2022: 123 · 2021: 96 · 2020: 39 · 2019: 11
FWCI: 24.53
Type: book
Language: en
Open access: closed
Licence: www.cambridge.org/core/terms (unspecified)
Locations: Cambridge University Press eBooks (publishedVersion)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
Social Sciences › Economics, Econometrics and Finance › Finance › Stochastic processes and financial applications
Keywords: measure-theoretic probability, law of large numbers, central limit theorem, random walks, martingales, Markov chains, ergodic theorem, Brownian motion, multidimensional Brownian motion, partial differential equations, Itô formula, stationary sequences

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