Probability Theory A Comprehensive Course /

• Main Author: Klenke, Achim (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London : Imprint: Springer, 2014.
• Edition: 2nd ed. 2014.
• Series: Universitext,
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Functional analysis.; Measure theory.; Probabilities.; Statistical physics.; Dynamical systems.; Probability Theory and Stochastic Processes.; Measure and Integration.; Dynamical Systems and Ergodic Theory.; Functional Analysis.; Statistical Physics, Dynamical Systems and Complexity.

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...

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.