Athreya / Lahiri Measure Theory and Probability Theory

2006
ISBN: 978-0-387-35434-7
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 632 Seiten, eBook

Reihe: Springer Texts in Statistics

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.

Zielgruppe

Research

Autoren/Hrsg.

Athreya, Krishna B.

Lahiri, Soumendra N.

Inhaltsverzeichnis

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 Processes.