Probability Theory (eBook)

A Comprehensive Course

Achim Klenke (Autor)

eBook Download: PDF

2013 | 2., nd ed. 2014
XII, 638 Seiten
Springer London (Verlag)
978-1-4471-5361-0 (ISBN)

Infos

This second edition of the popular textbook contains a comprehensive course in modern probability theory. It includes a wealth of examples and more than 270 exercises as well as biographic details of key mathematicians.

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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.

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 30.8.2013
• Reihe/Serie: Universitext
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
• Schlagworte: Brownian motion • Integration Theory • limit theorems • markov chains • Martingales • measure theory • percolation • Poisson Point Process • Statistical Physics • Stochastic differential equations • stochastic integral • Stochastic Processes
• ISBN-10: 1-4471-5361-8 / 1447153618
• ISBN-13: 978-1-4471-5361-0 / 9781447153610