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Foundations of modern probability

Author: Olav Kallenberg
Publisher: New York : Springer, 2002
Series: Probability and its Applications
Edition/Format:   Print book : English : 2. edView all editions and formats
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The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been  Read more...

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Document Type: Book
All Authors / Contributors: Olav Kallenberg
ISBN: 0387953132 9780387953137
OCLC Number: 472336372
Description: xvii, 638 s
Contents: * 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 * Appendix 1: Advanced Measure Theory * Appendix 2: Some Special Spaces * Historical and Bibliographical Notes * Bibliography * Indices
Series Title: Probability and its Applications

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"The second edition of this admirable book has grown by well over one hundred pages, including such new material as: multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Read more...

 
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