Hardcover. Etat : New. Contents: 1. Measure. 2. Signed measure. 3. Conditional expectation. 4. Martingales. 5. Almost sure and Lp convergence. 6. Application of convergence theorems. 7. Central limit theorem. 8. Additional Topics. 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. N� de r�f. du vendeur 139952A

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LITTLE BOOK OF MARTINGALES

RAJAT SUBHRA HAZRA ARUP BOSE, ARIJIT CHAKRABARTY

Edit� par HINDUSTAN, 2024

ISBN 10 : 8195782965 ISBN 13 : 9788195782963

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Vendeur : UK BOOKS STORE, London, LONDO, Royaume-Uni

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Hardcover. Etat : New. Brand New! Fast Delivery This is an International Edition and ship within 24-48 hours. Deliver by FedEx and Dhl, & Aramex, UPS, & USPS and we do accept APO and PO BOX Addresses. Order can be delivered worldwide within 7-12 days and we do have flat rate for up to 2LB. Extra shipping charges will be requested if the Book weight is more than 5 LB. This Item May be shipped from India, United states & United Kingdom. Depending on your location and availability. N� de r�f. du vendeur AD 9788195782963

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