Foundations of modern probability:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham, Switzerland
Springer
[2021]
|
| Edition: | Third edition |
| Series: | Probability theory and stochastic modelling
Volume 99 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Erscheint ab 3. Auflage 2-bändig |
| Physical Description: | 2 Bände |
| ISBN: | 9783030618704 9783030618735 |
Staff View
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Record in the Search Index
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| adam_text | Contents Introduction and Reading Guide — ------ 1 I. Measure Theoretic Prerequisites--------- 7 1. Sets and functions, measures and integration 9 2. Measure extension and decomposition 33 3. Kernels, disintegration, and invariance 55 II. Some Classical Probability Theory--------4- Processes, distributions, and independence 79 81 5, Random sequences, series, and averages 101 6. Gaussian and Poisson convergence 125 7. Infinite divisibility and general null arrays Ц7 III. Conditioning and Martingales--------- 161 8. Conditioning and disintegration 163 9. Optional times and martingales 185 10. Predictability and compensation 207 IV. Markovian and Related Structures--------- 231 11. Markov properties and discrete-time chains 233 12. Random walks and renewal processes 255 13. Jump-type chains and branching processes 277 V. Some Fundamental Processes--------- 295 14- Gaussian processes and Brownian motion 297 15. Poisson and related processes 321 16. Independent-increment and Lévy processes 345 17. Feller processes and semi-groups 367 VI. Stochastic Calculus and Applications--------- 393 18. Itô integration and quadratic variation 395 19. Continuous martingales and Brownian motion 417 20. Semi-martingales and stochastic integration 439 21. Malliavin calculus 465 xi
Foundations of Modern Probability xii VII. Convergence and Approximation--------- 487 22. Skorohod embedding and functional convergence 489 23. Convergence in distribution 505 24. Large deviations 529 VIII. Stationarity, Symmetry and Invariance--------- 555 25. Stationary processes and ergodic theorems 557 26. Ergodic properties of Markov processes 587 27. Symmetric distributions and predictable maps 611 28. Multi-variate arrays and symmetries 631 IX. Random Sets and Measures--------- 659 29. Local time, excursions, and additive functionals 661 30. Random measures, smoothing and scattering 685 31. Palm and Gibbs kernels, local approximation 709 X. SDEs, Diffusions, and Potential Theory--------- 733 32. Stochastic equations and martingale problems 735 33. One-dimensional SDEs and diffusions 751 34- PDE connections and potential theory 771 35. Stochastic differential geometry 801 Appendices--------1. 2. 3. 4. 5. 6. 7. 827 Measurable maps — 827, General topology — 828, Linear spaces — 831, Linear operators — 835, Function and measure spaces — 839, Classes and spaces of sets — 84Յ, Differential geometry — 847 Notes and References--------- 853 Bibliography--------- 889 Indices --------Authors 919, 919 Topics 925, Symbols 94Յ
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| adam_txt |
Contents Introduction and Reading Guide — ------ 1 I. Measure Theoretic Prerequisites--------- 7 1. Sets and functions, measures and integration 9 2. Measure extension and decomposition 33 3. Kernels, disintegration, and invariance 55 II. Some Classical Probability Theory--------4- Processes, distributions, and independence 79 81 5, Random sequences, series, and averages 101 6. Gaussian and Poisson convergence 125 7. Infinite divisibility and general null arrays Ц7 III. Conditioning and Martingales--------- 161 8. Conditioning and disintegration 163 9. Optional times and martingales 185 10. Predictability and compensation 207 IV. Markovian and Related Structures--------- 231 11. Markov properties and discrete-time chains 233 12. Random walks and renewal processes 255 13. Jump-type chains and branching processes 277 V. Some Fundamental Processes--------- 295 14- Gaussian processes and Brownian motion 297 15. Poisson and related processes 321 16. Independent-increment and Lévy processes 345 17. Feller processes and semi-groups 367 VI. Stochastic Calculus and Applications--------- 393 18. Itô integration and quadratic variation 395 19. Continuous martingales and Brownian motion 417 20. Semi-martingales and stochastic integration 439 21. Malliavin calculus 465 xi
Foundations of Modern Probability xii VII. Convergence and Approximation--------- 487 22. Skorohod embedding and functional convergence 489 23. Convergence in distribution 505 24. Large deviations 529 VIII. Stationarity, Symmetry and Invariance--------- 555 25. Stationary processes and ergodic theorems 557 26. Ergodic properties of Markov processes 587 27. Symmetric distributions and predictable maps 611 28. Multi-variate arrays and symmetries 631 IX. Random Sets and Measures--------- 659 29. Local time, excursions, and additive functionals 661 30. Random measures, smoothing and scattering 685 31. Palm and Gibbs kernels, local approximation 709 X. SDEs, Diffusions, and Potential Theory--------- 733 32. Stochastic equations and martingale problems 735 33. One-dimensional SDEs and diffusions 751 34- PDE connections and potential theory 771 35. Stochastic differential geometry 801 Appendices--------1. 2. 3. 4. 5. 6. 7. 827 Measurable maps — 827, General topology — 828, Linear spaces — 831, Linear operators — 835, Function and measure spaces — 839, Classes and spaces of sets — 84Յ, Differential geometry — 847 Notes and References--------- 853 Bibliography--------- 889 Indices --------Authors 919, 919 Topics 925, Symbols 94Յ |
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| dewey-full | 519.2 519.221 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-sort | 3519.2 |
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| discipline | Mathematik |
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| edition | Third edition |
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| index_date | 2024-07-03T17:17:21Z |
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| isbn | 9783030618704 9783030618735 |
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| spelling | Kallenberg, Olav Verfasser (DE-588)10837615X aut Foundations of modern probability Olav Kallenberg Third edition Cham, Switzerland Springer [2021] © 2021 2 Bände txt rdacontent n rdamedia nc rdacarrier Probability theory and stochastic modelling Volume 99 Erscheint ab 3. Auflage 2-bändig Probabilidades Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Erscheint auch als Online-Ausgabe 978-3-030-61871-1 (DE-604)BV047175289 Vorangegangen ist 2. edition 2002 0-387-95313-2 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032685270&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kallenberg, Olav Foundations of modern probability Probabilidades Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4079013-7 |
| title | Foundations of modern probability |
| title_auth | Foundations of modern probability |
| title_exact_search | Foundations of modern probability |
| title_exact_search_txtP | Foundations of modern probability |
| title_full | Foundations of modern probability Olav Kallenberg |
| title_fullStr | Foundations of modern probability Olav Kallenberg |
| title_full_unstemmed | Foundations of modern probability Olav Kallenberg |
| title_short | Foundations of modern probability |
| title_sort | foundations of modern probability |
| topic | Probabilidades Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Probabilidades Probabilities Wahrscheinlichkeitstheorie |
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