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Probability theory : a comprehensive course

Author: Achim Klenke
Publisher: London : Springer, ©2008.
Series: Universitext.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"Probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us to understand magnetism, amorphous media, genetic diversity and the perils of random developments on the financial markets, and they guide us in constructing more efficient algorithms." "This text is a comprehensive course in modern probability theory and its  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Klenke, Achim.
Probability theory.
London : Springer, ©2008
(DLC) 2007939558
(OCoLC)212893492
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Achim Klenke
ISBN: 9781848000483 1848000480 9781848000476 1848000472
OCLC Number: 233973008
Description: 1 online resource (xii, 616 pages) : illustrations.
Contents: Basic Measure Theory --
Independence --
Generating Functions --
The Integral --
Moments and Laws of Large Numbers --
Convergence Theorems --
Lp-Spaces and 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 --
Characteristics Functions and 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 Itô Integral --
Stochastic Differential Equations --
References --
Notation Index --
Name Index --
Subject Index.
Series Title: Universitext.
Other Titles: Wahrscheinlichkeitstheorie.
Responsibility: Achim Klenke.

Abstract:

Aimed primarily at graduate students and researchers, this text is a comprehensive course in modern probability theory and its measure-theoretical foundations. It covers a wide variety of topics,  Read more...

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From the reviews: "The book is indeed comprehensive, consisting of 26 chapters on different topics. ... can be well used as a reference book on a wide range of topics. The target audience is Read more...

 
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