TY  - BOOK
AU  - Bose,Arup
AU  - Chakrabarty,Arijit
AU  - Hazra,Rajat Subhra
TI  - Little book of martingales
T2  - Texts and readings in mathematics ; 
SN  - 9788195782963
U1  - 519.216.8 
PY  - 2024///
CY  - New Delhi : 
PB  - Hindustan Book Agency
KW  - Martingales (Mathematics)
KW  - Probability theory
KW  - Stochastic processes
KW  - Kesten-Stigum theorem
KW  - Radon-Nikodym theorem
N1  - Includes bibliographical references and indexes
N2  - This little book, suitable for masters and Ph.D. programs, covers basic results on discrete time martingales and their applications. It includes some additional interesting and useful topics. Adequate details are provided, with exercises within the text and at the end of chapters.

Basic results include Doob's optional sampling theorem, Wald identities, Doob's maximal inequality, upcrossing lemma, time-reversed martingales, a variety of convergence results, and a limited discussion of the Burkholder inequalities. Applications include the 0-1 laws of Kolmogorov and Hewitt-Savage, the strong laws for U-statistics and for exchangeable sequences, de-Finetti's theorem for exchangeable sequences, and Kakutani's theorem for product martingales. A simple central limit theorem for martingales is proven and applied to a basic urn model, the trace of a random matrix, and Markov chains. Some of the additional topics covered are forward martingale representation for U-statistics, conditional Borel-Cantelli lemma, Azuma-Hoeffding inequality, conditional three series theorem, strong law for martingales, and the Kesten-Stigum theorem for a simple branching process.

A first course in measure theoretic probability is a prerequisite. We have recollected its essential concepts and results, mostly without proofs
UR  - https://www.hindbook.com/images/trim86_content.pdf
UR  - https://www.goodreads.com/book/show/213786398-a-little-book-of-martingales#CommunityReviews
ER  -