2019/04/05 by Rick Durrett · 2 citations
Mathematics · #Benford’s Law and Fraud Detection #Probability and Statistical Research #Stochastic processes and statistical mechanics #Ergodic theory #Mathematics #Mathematical proof #Probability theory #Brownian motion #Central limit theorem #Calculus (dental) #Limit (mathematics) #Random walk #Stochastic differential equation #Markov chain #Discrete mathematics #Mathematical economics #Pure mathematics #Applied mathematics #Mathematical analysis
paper · doi:10.1017/9781108591034
openalex publication_date 2019/04/05 · openalex created_date 2022/02/13 · openalex updated_date 2026/07/30
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.