Probability Theory A Comprehensive Course /

This second edition of the popular textbook contains a comprehensive course in modern probability theory. Overall, probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us in understanding magnetism, amorpho...

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Bibliographic Details
Published in:Springer eBooks
Main Author: Klenke, Achim (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: London : Springer London : Imprint: Springer, 2014.
Edition:2nd ed. 2014.
Series:Universitext,
Subjects:
Online Access:http://dx.doi.org/10.1007/978-1-4471-5361-0
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Table of Contents:
  • 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 Itˆo Integral
  • Stochastic Differential Equations.