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
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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“Sample size impacts pattern detection, following the Central Limit Theorem [10].”
From Mathematical proof of the Fisher-Escolà Q statistical distribution in quantum consciousness modeling (2025) · cites this paper as [10]
Citations
Cites
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Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire
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Independent and stationary sequences of random variables
Ibragimov, I. A., Ліннік, Ю. В., & Kingmán, J. F. C. (1971) · Cited by 2,049
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The Granular Origins of Aggregate Fluctuations
Gabaix, X. (2011) · Econometrica · doi:10.3982/ecta8769 · Cited by 1,388
Deep Concatenated Residual Network With Bidirectional LSTM for One-Hour-Ahead Wind Power Forecasting
Ko, M.-S., Lee, K., Kim, J.-K., Hong, C. W., Dong, Z. Y., & Hur, K. (2020) · IEEE Transactions on Sustainable Energy · doi:10.1109/tste.2020.3043884 · Cited by 273
Fiscal Rules and Discretion Under Persistent Shocks
Halac, M., & Yared, P. (2014) · Econometrica · doi:10.3982/ecta11207 · Cited by 160
Noise Suppression With Similarity-Based Self-Supervised Deep Learning
Niu, C., Li, M., Fan, F., Wu, W., Guo, X., Lyu, Q., & Wang, G. (2022) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2022.3231428 · Cited by 119
Liu, M., Liu, Z., Chu, F., Zheng, F., & Chu, C. (2020) · International Journal of Production Research · doi:10.1080/00207543.2020.1841318 · Cited by 91
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
- 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
- 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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