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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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Research works printed but not linked: 20

  1. Vershik, 1977, Asymptotic behavior of the Plancherel measure of the symmetric group and the limit form of random Young tableau, Dokl. Akad. Nauk SSR, 233, 1024
  2. Revuz, 1984, Markov Chains
  3. Smirnov, 1949, Limit distributions for the terms of a variational series, AMS Transl. Series., 1
  4. Neveu, 1965, Mathematical Foundations of the Calculus of Probabilities
  5. Lindenbaum, 1926, Contributions à l’étude de l’espace metrique, Fund. Math., 8, 209
  6. Freedman, 1971, Markov chains
  7. Dieudonné, 1948, Sur la théore`me de Lebesgue-Nikodym, II, Ann. Univ. Grenoble., 23, 25
  8. Liggett, 2010, Continuous Tiem Markov Processes. An Introduction
  9. 10.1007/978-1-4757-4229-9 · DOI
  10. Benford, 1938, The law of anomalous numbers, Proc. Amer. Phil. Soc., 78, 552
  11. Andersen, 1984, On the introduction of measures in infinite product spaces, Danske Vid. Selsk. Mat.-Fys. Medd., 25
  12. Royden, 1988, Real Analysis
  13. Breiman, 1968, Probability
  14. Oseledĕc, 1968, A multiplicative ergodic theorem. Lyapunov characteristic numbers for synmaical systems, Trans. Moscow Math. Soc., 19, 197
  15. Doob, 1953, Stochastic Processes
  16. Garsia, 1965, A simple proof of E. Hopf’s maximal ergodic theorem, J. Math. Mech., 14, 381
  17. Furstenburg, 1970, Advances in Probability
  18. Lévy, 1937, Théorie de lladdition des variables aléatoires
  19. Blumenthal, 1968, Markov Processes and Their Potential Theory
  20. Kesten, 1986, École d’été de probabilités de Saint-Flour XIV

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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 · 2018: 2 · 2017: 1 · 2016: 1 · 2014: 1 · 2012: 1
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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