Probability theory : a comprehensive course
Author(s)
Bibliographic Information
Probability theory : a comprehensive course
（Universitext）
Springer, c2008
- Other Title
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Wahrscheinlichkeitstheorie
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Note
Originally published: Berlin : Springer, c2006
Includes bibliographical reference (p. [591]-598) and indexes
Description and Table of Contents
Description
Aimed primarily at graduate students and researchers, this text is a comprehensive course in modern probability theory and its measure-theoretical foundations. It covers a wide variety of topics, many of which are not usually found in introductory textbooks. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in the world of probability theory. In addition, plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation.
Table of Contents
Basic Measure Theory.- Independence.- Generating Functions.- The Integral.- Moments and Laws of Large Numbers.- Convergence Theorems.- Lp-Spaces and Radon-Nikodym Theorem.- Conditional Expectations.- Martingales.- Optional Sampling Theorems.- Martingale Convergence Theorems and their Applications.- Backwards Martingales and Exchangeability.- Convergence of Measures.- Probability Measures on Product Spaces.- Characteristics Functions and Central Limit Theorem.- Infinitely Divisible Distributions.- Markov Chains.- Convergence of Markov Chains.- Markov Chains and Electrical Networks.- Ergodic Theory.- Brownian Motion.- Law of the Iterated Logarithm.- Large Deviations.- The Poisson Point Process.- The Ito Integral.- Stochastic Differential Equations.- References.- Notation Index.- Name Index.- Subject Index.
by "Nielsen BookData"