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Bibliographic Details
Main Author:	Galambos, János 1940-2019 (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Dekker 1995
Edition:	2. ed., rev. and expanded
Series:	Probability, pure and applied 10
Subjects:	Probabilidades Probabilités Processus stochastiques Variables aléatoires Probabilities Wahrscheinlichkeitstheorie Wahrscheinlichkeitsrechnung Einführung
Links:	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
Physical Description:	IX, 461 S.
ISBN:	0824793323

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MARC


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Record in the Search Index

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adam_text	ADVANCED PROBABILITY THEORY SECOND EDITION, REVISED AND EXPANDED JANOS GALAMBOS TEMPLE UNIVERSITY PHILADELPHIA, PENNSYLVANIA MARCEL DEKKER, INC. NEW YORKBASEL 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
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isbn	0824793323
language	English
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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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work_keys_str_mv	AT galambosjanos advancedprobabilitytheory

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