Foundations of Modern Probability

ISBN-10: 0387953132

ISBN-13: 9780387953137

Edition: 2nd 2002 (Revised)

Authors: Olav Kallenberg

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Description:

About the first edition: To sum it up, one can perhaps see a distinction among advanced probability books into those which are original and path-breaking in content, such as Levy's and Doob's well-known examples, and those which aim primarily to assimilate known material, such as Loeve's and more recently Rogers and Williams'. Seen in this light, Kallenberg's present book would have to qualify as the assimilation of probability par excellence. It is a great edifice of material, clearly and ingeniously presented, without any non-mathematical distractions. Readers wishing to venture into it may do so with confidence that they are in very capable hands.- Mathematical ReviewsThis new edition contains four new chapters as well as numerous improvements throughout the text. There are new chapters on measure Theory-key results, ergodic properties of Markov processes and large deviations.
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Book details

List price: $119.00
Edition: 2nd
Copyright year: 2002
Publisher: Springer
Publication date: 1/8/2002
Binding: Hardcover
Pages: 638
Size: 6.50" wide x 9.75" long x 1.25" tall
Weight: 2.288
Language: English

Preface to the Second Edition
Preface to the First Edition
Measure Theory - Basic Notions
Measure Theory - Key Results
Processes, Distributions, and Independence
Random Sequences, Series, and Averages
Characteristic Functions and Classical Limit Theorems
Conditioning and Disintegration
Martingales and Optional Times
Markov Processes and Discrete-Time Chains
Random Walks and Renewal Theory
Stationary Processes and Ergodic Theory
Special Notions of Symmetry and Invariance
Poisson and Pure Jump-Type Markov Processes
Gaussian Processes and Brownian Motion
Skorohod Embedding and Invariance Principles
Independent Increments and Infinite Divisibility
Convergence of Random Processes, Measures, and Sets
Stochastic Integrals and Quadratic Variation
Continuous Martingales and Brownian Motion
Feller Processes and Semigroups
Ergodic Properties of Markov Processes
Stochastic Differential Equations and Martingale Problems
Local Time, Excursions, and Additive Functionals
One-dimensional SDEs and Diffusions
Connections with PDEs and Potential Theory
Predictability, Compensation, and Excessive Functions
Semimartingales and General Stochastic Integration
Large Deviations
Advanced Measure Theory
Some Special Spaces
Historical and Bibliographical Notes
Bibliography
Symbol Index
Author Index
Subject Index
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