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

The DOI matches its Crossref record; 136 of the 136 references it cites were found in a registry or an index.

Probability: Theory and Examples

Durrett, Rick·2019·Cambridge University Press eBooks
DOI 10.1017/9781108591034
Open this paper in CoChat — free account

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.

Overview

Integrity signals

Registry

Crossref · 10.1017/9781108591034

Cites

136 of 136 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Verification

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Citations

Cites

Show all 129 references

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

Cited by

Sorted by citations

Items 401–500 of 858

Related

See all

Metadata

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

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review