Advanced probability theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
1995
|
| Ausgabe: | 2. ed., rev. and expanded |
| Schriftenreihe: | Probability, pure and applied
10 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 461 S. |
| ISBN: | 0824793323 |
Internformat
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| 250 | |a 2. ed., rev. and expanded | ||
| 264 | 1 | |a New York [u.a.] |b Dekker |c 1995 | |
| 300 | |a IX, 461 S. | ||
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Datensatz im Suchindex
| _version_ | 1804125098733469696 |
|---|---|
| adam_text | ADVANCED PROBABILITY THEORY SECOND EDITION, REVISED AND EXPANDED JANOS
GALAMBOS TEMPLE UNIVERSITY PHILADELPHIA, PENNSYLVANIA MARCEL DEKKER,
INC. NEW YORK*BASEL* HONG KONG CONTENTS PREFACE TO THE SECOND EDITION HI
PREFACE TO THE FIRST EDITION V 1. REVIEW OF BASIC CONCEPTS 1 1.1 EVENTS
1 1.2 PROBABILITY 5 1.3 A METHOD OF CONSTRUCTING PROBABILITIES 12 1.4
CLASSICAL PROBABILITY SPACES 19 1.5 SIMPLE RANDOM VARIABLES 22 1.6
CONDITIONAL PROBABILITY: THE ELEMENTARY CASE 28 1.7 INDEPENDENCE OF
EVENTS 31 1.8 RANDOM VARIABLES, DISTRIBUTION FUNCTIONS 36 REFERENCES 42
2. EXPECTATION AND INTEGRAL, WEAK AND STRONG CONVERGENCE 43 2.1
DEFINITIONS OF EXPECTATION AND INTEGRAL 43 2.2 BASIC PROPERTIES OF
EXPECTATION 47 2.3 THE INEQUALITIES OF MARKOV, CHEBYSHEV, AND KOLMOGOROV
50 2.4 SEQUENCES OF INTEGRALS 55 VLL VIII CONTENTS 2.5 THE STRONG LAW OF
LARGE NUMBERS: THE PROOF OF THEOREM 1 59 2.6 ZERO-ONE LAWS 63 2.7
LEBESGUE-STIELTJES INTEGRALS 68 2.8 WEAK CONVERGENCE 77 2.9 SPECIAL
DISTRIBUTION FUNCTIONS: PART I 83 REFERENCES 95 3. TRANSFORMS OF
DISTRIBUTION 97 3.1 CHARACTERISTIC FUNCTIONS: BASIC PROPERTIES 97 3.2
CHARACTERISTIC FUNCTIONS: THE UNIQUENESS AND CONTINUITY THEOREMS 105 3.3
CLASSICAL FORMS OF THE CENTRAL LIMIT THEOREM, AND A MODEL FOR
MEASUREMENT ERRORS 118 3.4 CHARACTERISTIC FUNCTIONS: INEQUALITIES 127
3.5 MULTIVARIATE CHARACTERISTIC FUNCTIONS 134 3.6 LAPLACE TRANSFORMS 136
3.7 GENERATING FUNCTIONS 140 3.8 SPECIAL DISTRIBUTIONS: PART II 144
REFERENCES 149 4. INFINITE SEQUENCES OF INDEPENDENT RANDOM VARIABLES:
WEAK CONVERGENCE 151 4.1 COMPLETE CONVERGENCE OF SUMS WITHOUT
NORMALIZATION, INFINITE SERIES 151 4.2 DECOMPOSITION OF THE NORMAL
DISTRIBUTION 162 4.3 LEVY S METRIC 165 4.4 ZOLOTAREV S THEOREM ON
ASYMPTOTIC NORMALITY, THE THEOREM OF LINDEBERG AND FELLER 172 4.5 SPEED
OF CONVERGENCE: THE BERRY-ESSEEN THEOREM 180 4.6 THE CLASS L OF LIMITING
DISTRIBUTIONS 186 REFERENCES 196 5. TRIANGULAR ARRAYS OF INDEPENDENT
RANDOM VARIABLES, INFINITELY DIVISIBLE DISTRIBUTIONS 198 5.1
INTRODUCTION 198 5.2 MORE ON INFINITELY DIVISIBLE DISTRIBUTIONS 203 5.3
CONVERGENCE UNDER UAN 211 5.4 CONVERGENCE TO SPECIAL DISTRIBUTIONS 218
5.5 SPECIAL DISTRIBUTIONS: PART III 230 REFERENCES 234 CONTENTS IX 6.
INDEPENDENT AND IDENTICALLY DISTRIBUTED RANDOM VARIABLES 236 6.1
CAUCHY S FUNCTIONAL EQUATION 237 6.2 STABLE DISTRIBUTIONS 242 6.3
REGULARLY VARYING FUNCTIONS 251 6.4 DOMAINS OF ATTRACTION FOR STABLE
DISTRIBUTIONS 256 6.5 THE ASYMPTOTIC THEORY OF THE EXTREMES 262 6.6 THE
LAW OF THE ITERATED LOGARITHM 277 6.7 MULTIVARIATE EXTENSION OF STABLE
DISTRIBUTIONS FOR SUMS AND EXTREMES 285 REFERENCES 289 7. CONDITIONAL
EXPECTATION; MARTINGALES 291 7.1 CONDITIONAL EXPECTATION, GIVEN A
DISCRETE RANDOM VARIABLE 292 7.2 RADON-NIKODYM THEOREM 296 7.3
CONDITIONAL EXPECTATION: THE GENERAL CASE 303 7.4 MARTINGALES 313 7.5 L
P SPACES 327 7.6 FURTHER LIMIT THEOREMS FOR MARTINGALES 333 7.7
EXCHANGEABILITY, DE FINETTI S THEOREM 344 REFERENCES 351 8. TOPICS IN
THE THEORY OF STOCHASTIC PROCESSES 353 8.1 FOUNDATIONS AND BASIC
CONCEPTS 353 8.2 POISSON PROCESS 358 8.3 RENEWAL PROCESSES 366 8.4 THE
GALTON-WATSON PROCESS; BUSY PERIODS IN QUEUES 375 8.5 MARKOV CHAINS 381
8.6 CONTINUOUS-TIME MARKOV CHAINS 392 8.7 AN INVARIANCE PRINCIPLE 401
REFERENCES 409 HINTS FOR SOLUTIONS OF EXERCISES 411 INDEX 453
|
| any_adam_object | 1 |
| author | Galambos, János 1940-2019 |
| author_GND | (DE-588)108371271 |
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| author_role | aut |
| author_sort | Galambos, János 1940-2019 |
| author_variant | j g jg |
| building | Verbundindex |
| bvnumber | BV010625663 |
| callnumber-first | Q - Science |
| callnumber-label | QA273 |
| callnumber-raw | QA273 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 800 |
| classification_tum | MAT 600f MAT 510f |
| ctrlnum | (OCoLC)32740007 (DE-599)BVBBV010625663 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed., rev. and expanded |
| format | Book |
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| indexdate | 2024-07-09T17:56:10Z |
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| isbn | 0824793323 |
| language | English |
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| physical | IX, 461 S. |
| publishDate | 1995 |
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| publisher | Dekker |
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| series | Probability, pure and applied |
| series2 | Probability, pure and applied |
| spelling | Galambos, János 1940-2019 Verfasser (DE-588)108371271 aut Advanced probability theory Janos Galambos 2. ed., rev. and expanded New York [u.a.] Dekker 1995 IX, 461 S. txt rdacontent n rdamedia nc rdacarrier Probability, pure and applied 10 Probabilidades Probabilités ram Processus stochastiques ram Variables aléatoires ram Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Wahrscheinlichkeitstheorie (DE-588)4079013-7 s 2\p DE-604 Probability, pure and applied 10 (DE-604)BV000844355 10 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007087468&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 | Galambos, János 1940-2019 Advanced probability theory Probability, pure and applied Probabilidades Probabilités ram Processus stochastiques ram Variables aléatoires ram Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4064324-4 (DE-588)4151278-9 |
| title | Advanced probability theory |
| title_auth | Advanced probability theory |
| title_exact_search | Advanced probability theory |
| title_full | Advanced probability theory Janos Galambos |
| title_fullStr | Advanced probability theory Janos Galambos |
| title_full_unstemmed | Advanced probability theory Janos Galambos |
| title_short | Advanced probability theory |
| title_sort | advanced probability theory |
| topic | Probabilidades Probabilités ram Processus stochastiques ram Variables aléatoires ram Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Probabilidades Probabilités Processus stochastiques Variables aléatoires Probabilities Wahrscheinlichkeitstheorie Wahrscheinlichkeitsrechnung Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007087468&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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