Foundations of modern probability : second edition

By: Olav KallenbergMaterial type: TextTextSeries: Probability and Its ApplicationsPublication details: Heidelberg: Springer-Verlag, [c2002]Edition: 2nd edDescription: 638 pISBN: 9780387953137Subject(s): MathematicsLOC classification: QA273Online resources: Click here to access online
Contents:
1. Measure Theory — Basic Notions 2. Measure Theory — Key Results 3. Processes, Distributions, and Independence 4. Random Sequences, Series, and Averages 5. Characteristic Functions and Classical Limit Theorems 6. Conditioning and Disintegration 7. Martingales and Optional Times 8. Markov Processes and Discrete-Time Chains 9. Random Walks and Renewal Theory 10. Stationary Processes and Ergodic Theory 11. Special Notions of Symmetry and Invariance 12. Poisson and Pure Jump-Type Markov Processes 13. Gaussian Processes and Brownian Motion 14. Skorohod Embedding and Invariance Principles 15. Independent Increments and Infinite Divisibility 16. Convergence of Random Processes, Measures, and Sets 17. Stochastic Integrals and Quadratic Variation 18. Continuous Martingales and Brownian Motion 19. Feller Processes and Semigroups 20. Ergodic Properties of Markov Processes 21. Stochastic Differential Equations and Martingale Problems 22. Local Time, Excursions, and Additive Functionals 23. One-Dimensional SDEs and Diffusions 24. Connections with PDEs and Potential Theory 25. Predictability, Compensation, and Excessive Functions 26. Semimartingales and General Stochastic Integration 27. Large Deviations
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1. Measure Theory — Basic Notions
2. Measure Theory — Key Results
3. Processes, Distributions, and Independence
4. Random Sequences, Series, and Averages
5. Characteristic Functions and Classical Limit Theorems
6. Conditioning and Disintegration
7. Martingales and Optional Times
8. Markov Processes and Discrete-Time Chains
9. Random Walks and Renewal Theory
10. Stationary Processes and Ergodic Theory
11. Special Notions of Symmetry and Invariance
12. Poisson and Pure Jump-Type Markov Processes
13. Gaussian Processes and Brownian Motion
14. Skorohod Embedding and Invariance Principles
15. Independent Increments and Infinite Divisibility
16. Convergence of Random Processes, Measures, and Sets
17. Stochastic Integrals and Quadratic Variation
18. Continuous Martingales and Brownian Motion
19. Feller Processes and Semigroups
20. Ergodic Properties of Markov Processes
21. Stochastic Differential Equations and Martingale Problems
22. Local Time, Excursions, and Additive Functionals
23. One-Dimensional SDEs and Diffusions
24. Connections with PDEs and Potential Theory
25. Predictability, Compensation, and Excessive Functions
26. Semimartingales and General Stochastic Integration
27. Large Deviations

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