Probability: theory and examples
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Belmont, Calif. [u.a.]
Wadsworth
1996
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 503 S. |
| ISBN: | 0534243185 |
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Datensatz im Suchindex
| _version_ | 1804125051304280064 |
|---|---|
| adam_text | A. N. SHIRYAEV PROBABILITY SECOND EDITION TRANSLATED BY R. P. BOAS WITH
54 ILLUSTRATIONS SPRINGER CONTENTS PREFACE TO THE SECOND EDITION VII
PREFACE TO THE FIRST EDITION IX INTRODUCTION 1 CHAPTER I ELEMENTARY
PROBABILITY THEORY 5 §1. PROBABILISTIC MODEL OF AN EXPERIMENT WITH A
FINITE NUMBER OF OUTCOMES 5 §2. SOME CLASSICAL MODELS AND DISTRIBUTIONS
17 §3. CONDITIONAL PROBABILITY. INDEPENDENCE 23 §4. RANDOM VARIABLES AND
THEIR PROPERTIES 32 §5. THE BERNOULLI SCHEME. I. THE LAW OF LARGE
NUMBERS 45 §6. THE BERNOULLI SCHEME. II. LIMIT THEOREMS (LOCAL, DE
MOIVRE-LAPLACE, POISSON) 55 §7. ESTIMATING THE PROBABILITY OF SUCCESS IN
THE BERNOULLI SCHEME 70 §8. CONDITIONAL PROBABILITIES AND MATHEMATICAL
EXPECTATIONS WITH RESPECT TO DECOMPOSITIONS 76 §9. RANDOM WALK. I.
PROBABILITIES OF RUIN AND MEAN DURATION IN COIN TOSSING 83 §10. RANDOM
WALK. II. REFLECTION PRINCIPLE. ARCSINE LAW 94 §11. MARTINGALES. SOME
APPLICATIONS TO THE RANDOM WALK 103 §12. MARKOV CHAINS. ERGODIC THEOREM.
STRONG MARKOV PROPERTY 110 CHAPTER II MATHEMATICAL FOUNDATIONS OF
PROBABILITY THEORY 131 §1. PROBABILISTIC MODEL FOR AN EXPERIMENT WITH
INFINITELY MANY OUTCOMES. KOLMOGOROV S AXIOMS 131 XIV CONTENTS §2.
ALGEBRAS AND CR-ALGEBRAS. MEASURABLE SPACES 139 §3. METHODS OF
INTRODUCING PROBABILITY MEASURES ON MEASURABLE SPACES 151 §4. RANDOM
VARIABLES. I. 170 §5. RANDOM ELEMENTS 176 §6. LEBESGUE INTEGRAL.
EXPECTATION 180 §7. CONDITIONAL PROBABILITIES AND CONDITIONAL
EXPECTATIONS WITH RESPECT TO A CR-ALGEBRA 212 §8. RANDOM VARIABLES. II.
234 §9. CONSTRUCTION OF A PROCESS WITH GIVEN FINITE-DIMENSIONAL
DISTRIBUTION 245 §10. VARIOUS KINDS OF CONVERGENCE OF SEQUENCES OF
RANDOM VARIABLES 252 §11. THE HILBERT SPACE OF RANDOM VARIABLES WITH
FINITE SECOND MOMENT 262 §12. CHARACTERISTIC FUNCTIONS 274 §13. GAUSSIAN
SYSTEMS 297 CHAPTER III CONVERGENCE OF PROBABILITY MEASURES. CENTRAL
LIMIT THEOREM 308 §1. WEAK CONVERGENCE OF PROBABILITY MEASURES AND
DISTRIBUTIONS 308 §2. RELATIVE COMPACTNESS AND TIGHTNESS OF FAMILIES OF
PROBABILITY DISTRIBUTIONS 317 §3. PROOFS OF LIMIT THEOREMS BY THE METHOD
OF CHARACTERISTIC FUNCTIONS 321 §4. CENTRAL LIMIT THEOREM FOR SUMS OF
INDEPENDENT RANDOM VARIABLES. I. THE LINDEBERG CONDITION 328 §5. CENTRAL
LIMIT THEOREM FOR SUMS OF INDEPENDENT RANDOM VARIABLES. II. NONCLASSICAL
CONDITIONS 337 §6. INFINITELY DIVISIBLE AND STABLE DISTRIBUTIONS 341 §7.
METRIZABILITY OF WEAK CONVERGENCE 348 §8. ON THE CONNECTION OF WEAK
CONVERGENCE OF MEASURES WITH ALMOST SURE CONVERGENCE OF RANDOM ELEMENTS
( METHOD OF A SINGLE PROBABILITY SPACE ) 353 §9. THE DISTANCE IN
VARIATION BETWEEN PROBABILITY MEASURES. KAKUTANI-HELLINGER DISTANCE AND
HELLINGER INTEGRALS. APPLICATION TO ABSOLUTE CONTINUITY AND SINGULARITY
OF MEASURES 359 §10. CONTIGUITY AND ENTIRE ASYMPTOTIC SEPARATION OF
PROBABILITY MEASURES 368 §11. RAPIDITY OF CONVERGENCE IN THE CENTRAL
LIMIT THEOREM 373 §12. RAPIDITY OF CONVERGENCE IN POISSON S THEOREM 376
CHAPTER IV SEQUENCES AND SUMS OF INDEPENDENT RANDOM VARIABLES 379 §1.
ZERO-OR-ONE LAWS 379 §2. CONVERGENCE OF SERIES 384 §3. STRONG LAW OF
LARGE NUMBERS 388 §4. LAW OF THE ITERATED LOGARITHM 395 §5. RAPIDITY OF
CONVERGENCE IN THE STRONG LAW OF LARGE NUMBERS AND IN THE PROBABILITIES
OF LARGE DEVIATIONS 400 CONTENTS XV CHAPTER V STATIONARY (STRICT SENSE)
RANDOM SEQUENCES AND ERGODIC THEORY 404 §1. STATIONARY (STRICT SENSE)
RANDOM SEQUENCES. MEASURE-PRESERVING TRANSFORMATIONS 404 §2. ERGODICITY
AND MIXING 407 §3. ERGODIC THEOREMS 409 L CHAPTER VI STATIONARY (WIDE
SENSE) RANDOM SEQUENCES. L 2 THEORY 415 §1. SPECTRAL REPRESENTATION OF
THE COVARIANCE FUNCTION 415 §2. ORTHOGONAL STOCHASTIC MEASURES AND
STOCHASTIC INTEGRALS 423 §3. SPECTRAL REPRESENTATION OF STATIONARY (WIDE
SENSE) SEQUENCES 429 §4. STATISTICAL ESTIMATION OF THE COVARIANCE
FUNCTION AND THE SPECTRAL DENSITY 440 §5. WOLD S EXPANSION 446 §6.
EXTRAPOLATION. INTERPOLATION AND FILTERING 453 §7. THE KALMAN-BUCY
FILTER AND ITS GENERALIZATIONS 464 CHAPTER VII SEQUENCES OF RANDOM
VARIABLES THAT FORM MARTINGALES 474 §1. DEFINITIONS OF MARTINGALES AND
RELATED CONCEPTS 474 §2. PRESERVATION OF THE MARTINGALE PROPERTY UNDER
TIME CHANGE AT A RANDOM TIME 484 §3. FUNDAMENTAL INEQUALITIES 492 §4.
GENERAL THEOREMS ON THE CONVERGENCE OF SUBMARTINGALES AND MARTINGALES
508 §5. SETS OF CONVERGENCE OF SUBMARTINGALES AND MARTINGALES 515 §6.
ABSOLUTE CONTINUITY AND SINGULARITY OF PROBABILITY DISTRIBUTIONS 524 §7.
ASYMPTOTICS OF THE PROBABILITY OF THE OUTCOME OF A RANDOM WALK WITH
CURVILINEAR BOUNDARY 536 §8. CENTRAL LIMIT THEOREM FOR SUMS OF DEPENDENT
RANDOM VARIABLES 541 §9. DISCRETE VERSION OF ITO S FORMULA 554 §10.
APPLICATIONS TO CALCULATIONS OF THE PROBABILITY OF RUIN IN INSURANCE 558
CHAPTER VIII SEQUENCES OF RANDOM VARIABLES THAT FORM MARKOV CHAINS 564
§1. DEFINITIONS AND BASIC PROPERTIES 564 §2. CLASSIFICATION OF THE
STATES OF A MARKOV CHAIN IN TERMS OF ARITHMETIC PROPERTIES OF THE
TRANSITION PROBABILITIES P { {F 569 §3. CLASSIFICATION OF THE STATES OF
A MARKOV CHAIN IN TERMS OF ASYMPTOTIC PROPERTIES OF THE PROBABILITIES P^
573 §4. ON THE EXISTENCE OF LIMITS AND OF STATIONARY DISTRIBUTIONS 582
§5. EXAMPLES 587 XVI CONTENTS HISTORICAL AND BIBLIOGRAPHICAL NOTES 596
REFERENCES 603 INDEX OF SYMBOLS 609 INDEX 611
|
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| spelling | Durrett, Richard 1951- Verfasser (DE-588)121396789 aut Probability theory and examples Richard Durrett 2. ed. Belmont, Calif. [u.a.] Wadsworth 1996 XIII, 503 S. txt rdacontent n rdamedia nc rdacarrier Verjetnost - Osnovna teorija Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s 2\p DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007055151&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Durrett, Richard 1951- Probability theory and examples Verjetnost - Osnovna teorija Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4079013-7 (DE-588)4143389-0 |
| title | Probability theory and examples |
| title_auth | Probability theory and examples |
| title_exact_search | Probability theory and examples |
| title_full | Probability theory and examples Richard Durrett |
| title_fullStr | Probability theory and examples Richard Durrett |
| title_full_unstemmed | Probability theory and examples Richard Durrett |
| title_short | Probability |
| title_sort | probability theory and examples |
| title_sub | theory and examples |
| topic | Verjetnost - Osnovna teorija Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Verjetnost - Osnovna teorija Wahrscheinlichkeitsrechnung Wahrscheinlichkeitstheorie Aufgabensammlung |
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