Verfügbarkeit: Solutions to problems: A first course in stochastic processes

Solutions to problems: A first course in stochastic processes:

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Bibliographische Detailangaben
Hauptverfasser:	Karlin, Samuel 1924-2007 (VerfasserIn), Taylor, Howard M. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	New York [u.a.] Acad. Press [1975]
Ausgabe:	2. ed.
Schlagworte:	Stochastic processes Stochastischer Prozess
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Erscheinungsjahr ermittelt
Beschreibung:	92 S. graph. Darst.
ISBN:	0123985536

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MARC


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Datensatz im Suchindex

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adam_text	A FIRST COURSE IN STOCHASTIC PROCESSES SECOND EDITION SAMUEL KARLIN HOWARD M. TAYLOR STANFORD UNIVERSITY CORNELL UNIVERSITY AND THE WEIZMANN INSTITUTE OF SCIENCE ACADEMIC PRESS NEW YORK SAN FRANCISCO LONDON A SUBSIDIARY OF HARCOURT BRACE JOVANOVICH , PUBLISHERS CONTENTS PREFACE .. .. . * .. .. .. .. XI PREFACE TO FIRST EDITION .. .. .. .. .. XV CHAPTER 1 ELEMENTS OF STOCHASTIC PROCESSES 1. REVIEW OF BASIC TERMINOLOGY AND PROPERTIES OF RANDOM VARIABLES AND DISTRIBUTION FUNCTIONS . . . . . . . . . . 1 2. TWO SIMPLE EXAMPLES OF STOCHASTIC PROCESSES . . . . . . 20 3. CLASSIFICATION OF GENERAL STOCHASTIC PROCESSES . . . . . . 26 4. DENNING A STOCHASTIC PROCESS . . . . . . . . . . 32 ELEMENTARY PROBLEMS . . . . . . . . . . 33 PROBLEMS . . . . . . . . . . . . 36 NOTES .. . . .. .. .. .. .. 44 REFERENCES . . .. . . . . . . . . 44 CHAPTER 2 MARKOV CHAINS 1. DEFINITIONS . . .. .. .. .. .. 45 2. EXAMPLES OF MARKOV CHAINS .. .. .. .. .. 47 3. TRANSITION PROBABILITY MATRICES OF A MARKOV CHAIN . . . . .. 58 VI CONTENTS 4. CLASSIFICATION OF STATES OF A MARKOV CHAIN . . . . . . .. 59 5. RECURRENCE . . . . . . . . . . .. 62 6. EXAMPLES OF RECURRENT MARKOV CHAINS .. . . .. .. 67 7. MORE ON RECURRENCE .. .. .. . . .. .. 72 ELEMENTARY PROBLEMS . . . . . . . . 73 PROBLEMS . . . . .. . . . . . . 77 NOTES .. .. .. .. .. .. .. 79 REFERENCES . . . . . . .. . . . . 80 CHAPTER 3 THE BASIC LIMIT THEOREM OF MARKOV CHAINS AND APPLICATIONS 1. DISCRETE RENEWAL EQUATION . . . . .. . . . . 81 2. PROOF OF THEOREM 1.1 .. .. .. .. .. 87 3. ABSORPTION PROBABILITIES . . . . . . . . . . 89 4. CRITERIA FOR RECURRENCE . . . . . . . . . . 94 5. A QUEUEING EXAMPLE .. .. .. .. .. 96 6. ANOTHER QUEUEING MODEL . . . . . . . . . . 102 7. RANDOM WALK .. .. .. .. .. .. 106 ELEMENTARY PROBLEMS . . .. . . . . . . 108 PROBLEMS . . . . . . . . . . . . 112 NOTES .. .. .. .. .. .. .. 116 REFERENCE .. .. .. .. .. .. 116 CHAPTER 4 CLASSICAL EXAMPLES OF CONTINUOUS TIME MARKOV CHAINS 1. GENERAL PURE BIRTH PROCESSES AND POISSON PROCESSES .. .. .. 117 2. MORE ABOUT POISSON PROCESSES .. .. .. .. .. 123 3. A COUNTER MODEL .. .. .. .. .. .. 128 4. BIRTH AND DEATH PROCESSES .. .. .. .. .. 131 5. DIFFERENTIAL EQUATIONS OF BIRTH AND DEATH PROCESSES . . . . . . 135 6. EXAMPLES OF BIRTH AND DEATH PROCESSES . . . . . . . . 137 7. BIRTH AND DEATH PROCESSES WITH ABSORBING STATES . . . . . . 145 8. FINITE STATE CONTINUOUS TIME MARKOV CHAINS . . . . . . 150 ELEMENTARY PROBLEMS . . . . . . . . . . 152 PROBLEMS . . . . . . . . . . . . 158 NOTES .. .. .. .. .. .. .. 165 REFERENCES . . . . . . . . . . .. 166 CONTENTS ~ VII CHAPTER 5 RENEWAL PROCESSES 1. DEFINITION OF A RENEWAL PROCESS AND RELATED CONCEPTS . . . . 167 2. SOME EXAMPLES OF RENEWAL PROCESSES .. . . . . . . 170 3. MORE ON SOME SPECIAL RENEWAL PROCESSES . . . . . . . . 173 4. RENEWAL EQUATIONS AND THE ELEMENTARY RENEWAL THEOREM . . . . 181 5. THE RENEWAL THEOREM .. .. .. .. . . 189 6. APPLICATIONS OF THE RENEWAL THEOREM . . . . . . . . 192 7. GENERALIZATIONS AND VARIATIONS ON RENEWAL PROCESSES . . . . . . 197 8. MORE ELABORATE APPLICATIONS OF RENEWAL THEORY . . . . . . 212 9. SUPERPOSITION OF RENEWAL PROCESSES . . . . . . . . 221 ELEMENTARY PROBLEMS . . . . . . . . . . 228 PROBLEMS . . .. . . . . . . . . 230 REFERENCE .. .. .. .. .. . . 237 CHAPTER 6 MARTINGALES 1. PRELIMINARY DEFINITIONS AND EXAMPLES . . . . . . . . 238 2. SUPERMARTINGALES AND SUBMARTINGALES . . . . . . . . 248 3. THE OPTIONAL SAMPLING THEOREM . . . . . . . , 253 4. SOME APPLICATIONS OF THE OPTIONAL SAMPLING THEOREM . . . . . . 263 5. MARTINGALE CONVERGENCE THEOREMS . . . . . . . . 278 6. APPLICATIONS AND EXTENSIONS OF THE MARTINGALE CONVERGENCE THEOREMS . . 287 7. MARTINGALES WITH RESPECT TO 8. OTHER MARTINGALES . . . . . . . . . . . . 313 ELEMENTARY PROBLEMS . . . . . . . . . . 325 PROBLEMS . . . . . . .. . . . . 330 NOTES .. .. .. . . .. . X . .. 339 REFERENCES . . . . . . . . . . . . 339 CHAPTER 7 BROWNIAN MOTION 1. BACKGROUND MATERIAL .. .. .. .. .. 340 2. JOINT PROBABILITIES FOR BROWNIAN MOTION . . . . . . . . 343 3. CONTINUITY OF PATHS AND THE MAXIMUM VARIABLES . . .. . . 345 4. VARIATIONS AND EXTENSIONS . . . . . . . . .. 351 5. COMPUTING SOME FUNCTIONALS OF BROWNIAN MOTION BY MARTINGALE METHODS . . 357 6. MULTIDIMENSIONAL BROWNIAN MOTION .. .. . . . . 365 7. BROWNIAN PATHS . . . . .. . . . . . . 371 VIII CONTENTS ELEMENTARY PROBLEMS .. .. .. .. .. 383 PROBLEMS . . .. . . . . .. . . 386 NOTES .. .. .. ... .. .. .. 391 REFERENCES . . . . .. .. .. .. 391 CHAPTER 8 BRANCHING PROCESSES 1. DISCRETE TIME BRANCHING PROCESSES . . . . . . .. 392 2. GENERATING FUNCTION RELATIONS FOR BRANCHING PROCESSES .. .. 394 3. EXTINCTION PROBABILITIES .. .. .. .. .. 396 4. EXAMPLES .. .. .. .. .. .. 400 5. TWO-TYPE BRANCHING PROCESSES .. .. .. .. .. 404 6. MULTI-TYPE BRANCHING PROCESSES .. .. .. .. 411 7. CONTINUOUS TIME BRANCHING PROCESSES .. .. .. .. 412 8. EXTINCTION PROBABILITIES FOR CONTINUOUS TIME BRANCHING PROCESSES .. .. 416 9. LIMIT THEOREMS FOR CONTINUOUS TIME BRANCHING PROCESSES . . . . 419 10. TWO-TYPE CONTINUOUS TIME BRANCHING PROCESS . . . . . . 424 11. BRANCHING PROCESSES WITH GENERAL VARIABLE LIFETIME . . . . .. 431 ELEMENTARY PROBLEMS . . . . . . . . .. 436 PROBLEMS .. .. .. .. .. . . 4 3 8 NOTES .. .. .. .. .. .. .. 442 REFERENCE . . . . . . . . .. . . 442 CHAPTER 9 STATIONARY PROCESSES 1. DEFINITIONS AND EXAMPLES . . . . . . . . . . 443 2. MEAN SQUARE DISTANCE . . . . .. . . * 451 3. MEAN SQUARE ERROR PREDICTION .. .. .. .. .. 461 4. PREDICTION OF COVARIANCE STATIONARY PROCESSES .. .. .. 470 5. ERGODIC THEORY AND STATIONARY PROCESSES .. .. .. .. 474 6. APPLICATIONS OF ERGODIC THEORY .. .. .. . * 489 7. SPECTRAL ANALYSIS OF COVARIANCE STATIONARY PROCESSES .. .. ** .. 502 8. GAUSSIAN SYSTEMS . . .. . . . . . . . * 510 9. STATIONARY POINT PROCESSES .. .. .. .. .. 516 10. THE LEVEL-CROSSING PROBLEM . . . . . . . . . . 519 ELEMENTARY PROBLEMS . . . . . . .. . . 524 PROBLEMS .. .. .. .. . . . . 527 NOTES .. .. .. .. .. .. .. 534 REFERENCES .. .. .. .. * * * * 535 CONTENTS ~ IX APPENDIX REVIEW OF MATRIX ANALYSIS 1. THE SPECTRAL THEOREM .. .. .. .. .. 536 2. THE FROBENIUS THEORY OF POSITIVE MATRICES .. .. .. .. 542 INDEX .. .. .. .. . * .* * * 553
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author	Karlin, Samuel 1924-2007 Taylor, Howard M.
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spelling	Karlin, Samuel 1924-2007 Verfasser (DE-588)118918672 aut Solutions to problems: A first course in stochastic processes Samuel Karlin ; Howard M. Taylor 2. ed. New York [u.a.] Acad. Press [1975] 92 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Erscheinungsjahr ermittelt Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s DE-604 Taylor, Howard M. Verfasser aut HEBIS Datenaustausch Mainz application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002203072&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Karlin, Samuel 1924-2007 Taylor, Howard M. Solutions to problems: A first course in stochastic processes Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd
subject_GND	(DE-588)4057630-9
title	Solutions to problems: A first course in stochastic processes
title_auth	Solutions to problems: A first course in stochastic processes
title_exact_search	Solutions to problems: A first course in stochastic processes
title_full	Solutions to problems: A first course in stochastic processes Samuel Karlin ; Howard M. Taylor
title_fullStr	Solutions to problems: A first course in stochastic processes Samuel Karlin ; Howard M. Taylor
title_full_unstemmed	Solutions to problems: A first course in stochastic processes Samuel Karlin ; Howard M. Taylor
title_short	Solutions to problems: A first course in stochastic processes
title_sort	solutions to problems a first course in stochastic processes
topic	Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd
topic_facet	Stochastic processes Stochastischer Prozess
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002203072&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT karlinsamuel solutionstoproblemsafirstcourseinstochasticprocesses AT taylorhowardm solutionstoproblemsafirstcourseinstochasticprocesses

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