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-20% su kodu: BOOKS
79,18 
Įprasta kaina: 98,98 
-20% su kodu: BOOKS
Kupono kodas: BOOKS
Akcija baigiasi: 2025-03-16
-20% su kodu: BOOKS
79,18 
Įprasta kaina: 98,98 
-20% su kodu: BOOKS
Kupono kodas: BOOKS
Akcija baigiasi: 2025-03-16
-20% su kodu: BOOKS
2025-03-31 79.18 InStock
Nemokamas pristatymas į paštomatus per 11-15 darbo dienų užsakymams nuo 10,00 

Knygos aprašymas

This concise textbook, fashioned along the syllabus for master¿s and Ph.D. programmes, covers basic results on discrete-time martingales and applications. It includes additional interesting and useful topics, providing the ability to move beyond. 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 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. Additional topics include forward martingale representation for U-statistics, conditional Borel¿Cantelli lemma, AzumäHoeffding inequality, conditional three series theorem, strong law for martingales and the Kesten¿Stigum theorem for a simple branching process. The prerequisite for this course is a first course in measure theoretic probability. The book recollects its essential concepts and results, mostly without proof, but full details have been provided for the Radon¿Nikodym theorem and the concept of conditional expectation.

Informacija

Autorius: Arup Bose, Rajat Subhra Hazra, Arijit Chakrabarty,
Leidėjas: Springer Nature Singapore
Išleidimo metai: 2024
Knygos puslapių skaičius: 200
ISBN-10: 9819744717
ISBN-13: 9789819744718
Formatas: 241 x 160 x 16 mm. Knyga kietu viršeliu
Kalba: Anglų

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