Foundations of Modern Probability
From the reviews of the first editions: "... 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 i...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
2002, 2002
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| Edition: | 2nd ed. 2002 |
| Series: | Probability and Its Applications
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of 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