Bose, Arup creator Chakrabarty, Arijit Subhra Hazra, Rajat text New Delhi Hindustan Book Agency ©2024 monographic eng

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xv, 206p. 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. Arup Bose, Arijit Chakrabarty and Rajat Subhra Hazra Probabilities Applied mathematics Probability theory Stochastic processes 519.21 BosL 9788195782963 260326 20260327183404.0