E-Book, Englisch, 621 Seiten, eBook
Reihe: Universitext
Klenke Probability Theory
1. Auflage 2007
ISBN: 978-1-84800-048-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
A Comprehensive Course
E-Book, Englisch, 621 Seiten, eBook
Reihe: Universitext
ISBN: 978-1-84800-048-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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, such as: limit theorems for sums of random variables; martingales; percolation; Markov chains and electrical networks; construction of stochastic processes; Poisson point processes and infinite divisibility; large deviation principles and statistical physics; Brownian motion; and stochastic integral and stochastic differential equations.
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.
Zielgruppe
Graduate
Autoren/Hrsg.
Weitere Infos & Material
Basic Measure Theory.- Independence.- Generating Functions.- The Integral.- Moments and Laws of Large Numbers.- Convergence Theorems.- Lp-Spaces and the 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.- Characteristic Functions and the 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 Itô Integral.- Stochastic Differential Equations.
