Foundations of modern probability

Olav Kallenberg

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 revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.

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[目次]

  • 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.

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この本の情報

書名 Foundations of modern probability
著作者等 Kallenberg, Olav
シリーズ名 Probability and its applications
出版元 Springer
刊行年月 c2002
版表示 2nd ed
ページ数 xvii, 638 p.
大きさ 24 cm
ISBN 9780387953137
NCID BA55715818
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言語 英語
出版国 アメリカ合衆国
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