Probability theory : a comprehensive course

Author(s)

• Klenke, Achim

Bibliographic Information

Probability theory : a comprehensive course

Achim Klenke

（Universitext）

Springer, c2014

2nd ed

Other Title

Wahrscheinlichkeitstheorie

Note

Originally published: Berlin : Springer, c2013

Includes bibliographical reference (p. 617-623) and indexes

Description and Table of Contents

Description

This second edition of the popular textbook contains a comprehensive course in modern probability theory, covering a wide variety of topics which are not usually found in introductory textbooks, including: * limit theorems for sums of random variables * martingales * percolation * Markov chains and electrical networks * construction of stochastic processes * Poisson point process and infinite divisibility * large deviation principles and statistical physics * Brownian motion * 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 probability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulations and some difficult proofs have been made more accessible. A wealth of examples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathematics and statistics in physics, computer science, economics and biology.

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 Ito Integral.- Stochastic Differential Equations.

by "Nielsen BookData"

Details

• NCID: BB13567449
• ISBN:
  • 9781447153603
• LCCN: 2013945095
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: ger
• Place of Publication: London
• Pages/Volumes: xii, 638 p.
• Size: 24 cm
• Classification:
  • LCC : QA273.18
  • DC22 : 519.2
• Subject Headings:
  • LCSH : Probabilities
• Parent Bibliography ID:
  • BA00021004