Measure Theory and Probability Theory

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This is a graduate level textbook on measure theory and probability theory. It presents the main concepts and results in measure theory and probability theory. It further provides heuristic explanations behind the theory to help students see the big picture.
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Measures and Integration: an Informal Introduction.- Measures.- Integration.- LP Spaces.- Differentiation.- Product Measures, Convolutions, and Transforms.- Probability Spaces.- Independence.- Laws of Large Numbers.- Convergence in Distribution.- Characteristic Functions.- Central Limit Theorems.- Conditional Expectation and Conditional Probability.- Discrete Parameter Martingales.- Markov Chains and MCMC.- Stochastic Processes.- Limit Theorems for Dependent Processes.- The Bootstrap.- Branching Process.
This is a graduate level textbook on measure theory and probability theory. It presents the main concepts and results in measure theory and probability theory in a simple and easy-to-understand way. It further provides heuristic explanations behind the theory to help students see the big picture. The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics. Prerequisites are kept to the minimal level and the book is intended primarily for first year Ph.D. students in mathematics and statistics.

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Autor: Krishna B. Athreya
ISBN-13 :: 9781441921918
ISBN: 1441921915
Erscheinungsjahr: 23.11.2010
Verlag: Springer New York
Gewicht: 963g
Seiten: 640
Sprache: Englisch
Auflage Softcover reprint of hardcover 1st ed. 2006
Sonstiges: Taschenbuch, 233x154x38 mm
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