Probability Theory : A Comprehensive Course /

This popular textbook, now in a revised and expanded third edition, presents a comprehensive course in modern probability theory. Probability plays an increasingly important role not only in mathematics, but also in physics, biology, finance and computer science, helping to understand phenomena such...

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Bibliographic Details
Main Author:	Klenke, Achim (Author)
Corporate Author:	SpringerLink (Online service)
Format:	eBook
Language:	English
Published:	Cham : Springer International Publishing : Imprint: Springer, 2020.
Edition:	3rd ed. 2020.
Series:	Universitext,
Subjects:	Probabilities. Measure theory. Dynamics. Ergodic theory. Vibration. Dynamical systems. Mathematical physics. Probability Theory and Stochastic Processes. Measure and Integration. Dynamical Systems and Ergodic Theory. Vibration, Dynamical Systems, Control. Theoretical, Mathematical and Computational Physics. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

1 Basic Measure Theory
2 Independence
3 Generating Functions
4 The Integral
5 Moments and Laws of Large Numbers
6 Convergence Theorems
7 Lp-Spaces and the Radon-Nikodym Theorem
8 Conditional Expectations
9 Martingales
10 Optional Sampling Theorems
11 Martingale Convergence Theorems and Their Applications
12 Backwards Martingales and Exchangeability
13 Convergence of Measures
14 Probability Measures on Product Spaces
15 Characteristic Functions and the Central Limit Theorem
16 Infinitely Divisible Distributions
17 Markov Chains
18 Convergence of Markov Chains
19 Markov Chains and Electrical Networks
20 Ergodic Theory
21 Brownian Motion
22 Law of the Iterated Logarithm
23 Large Deviations
24 The Poisson Point Process
25 The Itô Integral
26 Stochastic Differential Equations
References
Notation Index
Name Index
Subject Index.