Holdings: Evolution of systems in random media

Evolution of systems in random media:

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Bibliographic Details
Main Authors:	Koroljuk, Volodymyr S. 1925- (Author), Sviščuk, Anatolij (Author)
Format:	Book
Language:	English
Published:	Boca Raton [u.a.] CRC Pr. 1995
Subjects:	Mathematische Physik Stochastischer Prozess Markov-Prozess
Online Access:	Inhaltsverzeichnis
Physical Description:	352 S.
ISBN:	0849394058

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MARC


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adam_text	EVOLUTION OF SYSTEMS IN RANDOM MEDIA VLADIMIR KOROLYUK ANATOLY SWISHCHUK CRC PRESS BOCA RATON NEW YORK LONDON TOKYO CONTENTS PREFACE 5 INTRODUCTION 7 1 THE MARTINGALE PROBLEM AND WEAK CONVERGENCE IN A BANACH SPACE 13 1.1 RANDOM PROCESSES AND MARTINGALES IN A BANACH SPACE 13 1.2 OPERATOR SEMIGROUPS 25 1.2.1 DEFINITION AND BASIC PROPERTIES 25 1.2.2 EXAMPLES OF SEMIGROUPS 27 1.2.3 RESOLVENT OPERATOR 29 1.3 MARKOV PROCESSES. MARTINGALE CHARACTERIZATION 31 1.4 WEAK CONVERGENCE 36 1.5 MARTINGALE PROBLEM IN BANACH SPACE 42 2 MARKOV RENEWAL PROCESSES 53 2.1 SEMI-MARKOV PROCESSES 54 2.2 SINGULAR PERTURBED PROBLEMS 69 2.3 PERTURBATION OF REDUCIBLE-INVERTIBLE OPERATORS ... 71 2.4 PHASE MERGING OF SEMI-MARKOV PROCESSES 80 3 SEMI-MARKOV RANDOM EVOLUTIONS 93 3.1 DEFINITION AND CLASSIFICATION OF RANDOM EVOLUTIONS . 93 3.2 STOCHASTIC MODELS OF SYSTEMS 102 3.3 INHOMOGENEOUS SEMI-MARKOV RANDOM EVOLUTIONS . . 128 1 2 CONTENTS 4 WEAK CONVERGENCE OF RANDOM EVOLUTIONS 135 4.1 RELATIVE COMPACTNESS OF RANDOM EVOLUTIONS 136 4.1.1 WEAK COMPACTNESS IN THE AVERAGING THEOREM 139 4.1.2 WEAK COMPACTNESS IN THE DIFFUSION APPROXIMATION SCHEME 147 4.2 LIMITING EVOLUTIONS IN AVERAGING AND DIFFUSION AP- PROXIMATION SCHEMES 157 4.2.1 LIMITING REPRESENTATION IN THE AVERAGING SCHEME 158 4.2.2 LIMITING REPRESENTATION IN THE DIFFUSION AP- PROXIMATION SCHEME 166 4.2.3 STOCHASTIC INTEGRAL OPERATOR EQUATIONS IN DIF- FUSION APPROXIMATION 173 4.3 UNIQUENESS OF THE SOLUTION OF THE MARTINGALE PROBLEM 175 4.3.1 DUAL RANDOM EVOLUTION 175 4.3.2. AVERAGING THEOREM FOR DUAL RANDOM EVOLUTION 176 4.3.3 DIFFUSION APPROXIMATION THEOREM FOR DUAL RANDOM EVOLUTION 178 4.3.4 UNIQUENESS OF THE LIMITING SEMI-MARKOV RAN- DOM EVOLUTION IN THE DIFFUSION APPROXIMATION SCHEME 180 4.4. AVERAGING AND DIFFUSION APPROXIMATION OF RANDOM EVOLUTION IN REDUCIBLE RANDOM MEDIA 182 5 AVERAGING OF STOCHASTIC SYSTEMS IN SEMI-MARKOV RANDOM MEDIA 195 5.1 COMPACTS IN BANACH SPACES 195 5.2 TRAFFIC PROCESSES 198 5.3 IMPULSE TRAFFIC PROCESSES 204 5.4 ADDITIVE FUNCTIONALS 207 5.5 STOCHASTIC DIFFERENTIAL EQUATIONS 209 5.6 ADDITIVE FUNCTIONALS 211 5.7 [/-STATISTICAL PROCESSES 214 5.8 RANDOM EVOLUTIONS ON LIE GROUPS 216 CONTENTS 5.9 OSCILLATIONS OF A HARMONIC OSCILLATOR 218 5.10 WAVES IN CONDUCTORS AND BEAMS 221 6 DIFFUSION APPROXIMATION OF STOCHASTIC SYSTEMS 225 6.1 TRAFFIC PROCESS 225 6.2 IMPULSE TRAFFIC PROCESSES 228 6.3 ADDITIVE FUNCTIONALS 231 6.4 [/-STATISTICAL PROCESS 233 6.5 RANDOM MOTIONS ON LIE GROUPS 236 7 NORMAL DEVIATIONS OF SEMI-MARKOV RANDOM EVOLUTIONS 239 7.1 RANDOM EVOLUTION IN ERGODIC MEDIA 240 7.2 STOCHASTIC SYSTEMS 244 7.2.1 STORAGE PROCESS 244 7.2.2 TRAFFIC PROCESS 248 7.2.3 [/-STATISTICAL PROCESSES 249 7.2.4 INTEGRAL FUNCTIONALS 249 7.3 RANDOM EVOLUTION IN REDUCIBLE MEDIA 250 7.4 EVOLUTIONARY STOCHASTIC SYSTEMS IN REDUCIBLE MEDIA 253 7.4.1 STORAGE PROCESS 253 7.4.2 TRAFFIC PROCESS 255 7.4.3 [/-STATISTICAL PROCESS 256 7.4.4 INTEGRAL FUNCTIONALS 257 8 RATES OF CONVERGENCE IN THE LIMIT THEOREMS FOR RANDOM EVOLUTIONS 259 8.1 AVERAGING SCHEMES FOR RANDOM EVOLUTIONS 259 8.2 DIFFUSION APPROXIMATION SCHEME FOR RANDOM EVOLUTIONS 263 8.3 AVERAGING SCHEME FOR EVOLUTIONARY STOCHASTIC SYSTEMS IN RANDOM MEDIA 267 8.4 DIFFUSION APPROXIMATION SCHEME FOR EVOLUTIONARY STOCHASTIC SYSTEMS IN RANDOM MEDIA 275 9 STABILITY OF STOCHASTIC SYSTEMS 279 9.1 TRAFFIC PROCESS IN THE AVERAGING SCHEME 279 9.2 TRAFFIC PROCESS IN THE DIFFUSION APPROXIMATION SCHEME 286 4 CONTENTS 9.3 IMPULSE TRAFFIC PROCESS IN THE AVERAGING SCHEME . . . 292 9.4 IMPULSE TRAFFIC PROCESS IN THE DIFFUSION APPROXIMA- TION SCHEME 295 10 CONTROL OF EVOLUTIONARY STOCHASTIC SYSTEMS IN RANDOM MEDIA 299 10.1 FUNCTIONALS OF UNCONTROLLED PROCESSES 299 10.2 COST FUNCTIONALS 301 10.3 OPTIMAL STOCHASTIC CONTROL 305 BIBLIOGRAPHY 317 SUBJECT INDEX 347
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author	Koroljuk, Volodymyr S. 1925- Sviščuk, Anatolij
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isbn	0849394058
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spelling	Koroljuk, Volodymyr S. 1925- Verfasser (DE-588)119463717 aut Evolution of systems in random media Vladimir Korolyuk ; Anatoly Swishchuk Boca Raton [u.a.] CRC Pr. 1995 352 S. txt rdacontent n rdamedia nc rdacarrier Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Markov-Prozess (DE-588)4134948-9 s Sviščuk, Anatolij Verfasser (DE-588)1048087905 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007453790&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Koroljuk, Volodymyr S. 1925- Sviščuk, Anatolij Evolution of systems in random media Mathematische Physik (DE-588)4037952-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Markov-Prozess (DE-588)4134948-9 gnd
subject_GND	(DE-588)4037952-8 (DE-588)4057630-9 (DE-588)4134948-9
title	Evolution of systems in random media
title_auth	Evolution of systems in random media
title_exact_search	Evolution of systems in random media
title_full	Evolution of systems in random media Vladimir Korolyuk ; Anatoly Swishchuk
title_fullStr	Evolution of systems in random media Vladimir Korolyuk ; Anatoly Swishchuk
title_full_unstemmed	Evolution of systems in random media Vladimir Korolyuk ; Anatoly Swishchuk
title_short	Evolution of systems in random media
title_sort	evolution of systems in random media
topic	Mathematische Physik (DE-588)4037952-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Markov-Prozess (DE-588)4134948-9 gnd
topic_facet	Mathematische Physik Stochastischer Prozess Markov-Prozess
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007453790&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT koroljukvolodymyrs evolutionofsystemsinrandommedia AT sviscukanatolij evolutionofsystemsinrandommedia

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