Holdings: A first course in stochastic processes

A first course in stochastic processes:

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Bibliographic Details
Main Authors:	Karlin, Samuel 1924-2007 (Author), Taylor, Howard M. (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Academic Press [1975]
Edition:	Second edition
Subjects:	Processus stochastiques Stochastic Processes Stochastic processes Stochastik Stochastischer Prozess
Online Access:	Inhaltsverzeichnis
Item Description:	T. 2 u.d.T.: Karlin, Samuel: A second course in stochastic processes
Physical Description:	xvi, 557 Seiten Illustrationen
ISBN:	0123985528

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MARC


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Record in the Search Index

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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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spelling	Karlin, Samuel 1924-2007 (DE-588)118918672 aut A first course in stochastic processes Samuel Karlin ; Howard M. Taylor Second edition New York [u.a.] Academic Press [1975] © 1975 xvi, 557 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier T. 2 u.d.T.: Karlin, Samuel: A second course in stochastic processes Processus stochastiques Processus stochastiques ram Stochastic Processes Stochastic processes Stochastik (DE-588)4121729-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s DE-604 Stochastik (DE-588)4121729-9 s 1\p DE-604 Taylor, Howard M. (DE-588)171556046 aut Erscheint auch als Online-Ausgabe 978-0-08-057041-9 HEBIS Datenaustausch Mainz application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001499794&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
spellingShingle	Karlin, Samuel 1924-2007 Taylor, Howard M. A first course in stochastic processes Processus stochastiques Processus stochastiques ram Stochastic Processes Stochastic processes Stochastik (DE-588)4121729-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd
subject_GND	(DE-588)4121729-9 (DE-588)4057630-9
title	A first course in stochastic processes
title_auth	A first course in stochastic processes
title_exact_search	A first course in stochastic processes
title_full	A first course in stochastic processes Samuel Karlin ; Howard M. Taylor
title_fullStr	A first course in stochastic processes Samuel Karlin ; Howard M. Taylor
title_full_unstemmed	A first course in stochastic processes Samuel Karlin ; Howard M. Taylor
title_short	A first course in stochastic processes
title_sort	a first course in stochastic processes
topic	Processus stochastiques Processus stochastiques ram Stochastic Processes Stochastic processes Stochastik (DE-588)4121729-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd
topic_facet	Processus stochastiques Stochastic Processes Stochastic processes Stochastik Stochastischer Prozess
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001499794&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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