Random fragmentation and coagulation processes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2006
|
| Series: | Cambridge studies in advanced mathematics
102 |
| Subjects: | |
| Online Access: | Publisher description Table of contents only Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | vii, 280 p. ill. 24 cm |
| ISBN: | 0521867282 9780521867283 |
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Record in the Search Index
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| adam_text | RANDOM FRAGMENTATION AND COAGULATION PROCESSES JEAN BERTOIN LABORATOIRE
DE PROBABILITES ET MODELES ALEATOIRES UNIVERSITE PIERRE ET MARIE CURIE
CAMBRIDGE UNIVERSITY PRESS CONTENTS INTRODUCTION PAGE 1 1 SELF-SIMILAR
FRAGMENTATION CHAINS 6 1.1 CONSTRUCTION OF FRAGMENTATION CHAINS 6 1.1.1
PRELIMINARIES ON MARKOV CHAINS 7 1.1.2 BRANCHING MARKOV CHAINS 11 1.1.3
FRAGMENTATION CHAINS 16 1.2 GENEALOGICAL STRUCTURE 23 1.2.1 THE TREE OF
GENERATIONS 24 1.2.2 MALTHUSIAN HYPOTHESES AND THE INTRINSIC MARTINGALE
26 1.2.3 A RANDOMLY TAGGED BRANCH 31 1.3 EXTINCTION AND FORMATION OF
DUST FOR A 0 37 1.3.1 EXTINCTION 38 1.3.2 FORMATION OF DUST 40 1.4
SOME STRONG LAWS FOR A 0 43 1.4.1 A VARIATION OF THE LAW OF LARGE
NUMBERS * ^44 1.4.2 THE HOMOGENEOUS CASE (A = 0) * 46 1.4.3 THE CASE A
0 49 1.4.4 ANOTHER STRONG LAW VIA RENEWAL THEORY 53 1.5 ADDITIVE
MARTINGALES (HOMOGENEOUS CASE A = 0) 55 1.5.1 CONVERGENCE OF ADDITIVE
MARTINGALES 56 1.5.2 SOME APPLICATIONS 58 1.6 COMMENTS 62 2 RANDOM
PARTITIONS 66 2.1 MASS-PARTITIONS 66 2.1.1 PARTITIONS OF A UNIT MASS 66
2.1.2 INTERVAL-PARTITIONS 68 2.1.3 SIZE-BIASED SAMPLING AND REORDERING
71 VI CONTENTS 2.2 RANDOM MASS-PARTITIONS AND POISSON MEASURES 2.2.1
MULTIDIMENSIONAL DIRICHLET DISTRIBUTIONS 2.2.2 SOME PRELIMINARIES ON
POISSON RANDOM MEASURES 2.2.3 MASS-PARTITIONS INDUCED BY POISSON
MEASURES 2.2.4 GAMMA SUBORDINATORS AND DIRICHLET PROCESSES 2.2.5 STABLE
SUBORDINATORS AND POISSON-DIRICHLET PARTITIONS 2.3 EXCHANGEABLE RANDOM
PARTITIONS 2.3.1 SOME DEFINITION 2.3.2 KINGMAN S THEORY 2.3.3
EXCHANGEABLE PARTITION PROBABILITY FUNCTIONS 2.4 COMMENTS EXCHANGEABLE
FRAGMENTATIONS 3.1 HOMOGENEOUS FRAGMENTATION PROCESSES 3.1.1
FRAGMENTATION OF PARTITIONS 3.1.2 HOMOGENEOUS FRAGMENTATION AS MARKOV
PROCESSES 3.1.3 POISSONIAN STRUCTURE 3.2 ASYMPTOTIC FREQUENCIES 3.2.1
EROSION AND DISLOCATION 3.2.2 SUBORDINATOR REPRESENTATION OF THE TAGGED
FRAGMENT 3.2.3 LEVY-ITO DECOMPOSITION OF THE TAGGED FRAGMENT 3.3
SELF-SIMILAR FRAGMENTATIONS 3.3.1 DEFINITION AND FIRST PROPERTIES 3.3.2
CHANGING THE INDEX OF SELF-SIMILARITY 3.3.3 MASS-FRAGMENTATIONS 3.4
COMMENTS EXCHANGEABLE COALESCENTS .-- 4.1 KINGMAN S COALESCENT 4.1.1
GENEALOGY OF POPULATIONS IN THE WRIGHT-FISHER MODEL 4.1.2 CONSTRUCTION
OF KINGMAN S COALESCENT 4.1.3 INTERVAL REPRESENTATION OF KINGMAN S
COALESCENT 4.2 SIMULTANEOUS AND MULTIPLE COAGULATIONS 4.2.1 COAGULATION
OF PARTITIONS 4.2.2 EXCHANGEABLE COALESCENTS AND COAGULATION RATES 4.2.3
POISSONIAN CONSTRUCTION 4.2.4 CHARACTERIZATION OF COAGULATION RATES 4.3
EXCHANGEABLE MASS-COALESCENTS 4.3.1 MARKOV PROPERTY 4.3.2 DUST IN
EXCHANGEABLE MASS-COALESCENTS CONTENTS VII 4.4 SIMPLE COALESCENTS AND
FLOWS OF BRIDGES 189 4.4.1 COMPOSITIONS OF SIMPLE BRIDGES 190 4.4.2
FLOWS OF BRIDGES AND COAGULATION 196 4.4.3 THE DUAL FLOW AND A
POPULATION MODEL 200 4.4.4 THE BOLTHAUSEN-SZNITMAN COALESCENT 205 4.5
COMMENTS 211 ASYMPTOTIC REGIMES IN STOCHASTIC COALESCENCE 214 5.1
STOCHASTIC COALESCENCE 214 5.1.1 COALESCENT CHAINS 215 5.1.2 EXTENSION
TO INFINITE SYSTEMS 218 5.2 HYDRODYNAMIC BEHAVIOR AND SMOLUCHOWSKI S
EQUATIONS 226 5.2.1 THE MULTIPLICATIVE KERNEL 227 5.2.2
SUB-MULTIPLICATIVE KERNELS 235 5.3 THE ADDITIVE COALESCENCE 244 5.3.1
SOME BASIC PROPERTIES 244 5.3.2 COAGULATION OF TREES IN A RANDOM FOREST
247 5.3.3 THE STANDARD ADDITIVE COALESCENT 254 5.3.4 A DUAL
FRAGMENTATION PROCESS 258 5.4 COMMENTS 261 REFERENCES 264 LIST OF
SYMBOLS 276 INDEX 27 9
|
| adam_txt |
RANDOM FRAGMENTATION AND COAGULATION PROCESSES JEAN BERTOIN LABORATOIRE
DE PROBABILITES ET MODELES ALEATOIRES UNIVERSITE PIERRE ET MARIE CURIE
CAMBRIDGE UNIVERSITY PRESS CONTENTS INTRODUCTION PAGE 1 1 SELF-SIMILAR
FRAGMENTATION CHAINS 6 1.1 CONSTRUCTION OF FRAGMENTATION CHAINS 6 1.1.1
PRELIMINARIES ON MARKOV CHAINS 7 1.1.2 BRANCHING MARKOV CHAINS 11 1.1.3
FRAGMENTATION CHAINS 16 1.2 GENEALOGICAL STRUCTURE 23 1.2.1 THE TREE OF
GENERATIONS 24 1.2.2 MALTHUSIAN HYPOTHESES AND THE INTRINSIC MARTINGALE
26 1.2.3 A RANDOMLY TAGGED BRANCH 31 1.3 EXTINCTION AND FORMATION OF
DUST FOR A 0 37 1.3.1 EXTINCTION 38 1.3.2 FORMATION OF DUST 40 1.4
SOME STRONG LAWS FOR A 0 43 1.4.1 A VARIATION OF THE LAW OF LARGE
NUMBERS * ^44 1.4.2 THE HOMOGENEOUS CASE (A = 0) * 46 1.4.3 THE CASE A
0 49 1.4.4 ANOTHER STRONG LAW VIA RENEWAL THEORY 53 1.5 ADDITIVE
MARTINGALES (HOMOGENEOUS CASE A = 0) 55 1.5.1 CONVERGENCE OF ADDITIVE
MARTINGALES 56 1.5.2 SOME APPLICATIONS 58 1.6 COMMENTS ' 62 2 RANDOM
PARTITIONS 66 2.1 MASS-PARTITIONS 66 2.1.1 PARTITIONS OF A UNIT MASS 66
2.1.2 INTERVAL-PARTITIONS 68 2.1.3 SIZE-BIASED SAMPLING AND REORDERING
71 VI CONTENTS 2.2 RANDOM MASS-PARTITIONS AND POISSON MEASURES 2.2.1
MULTIDIMENSIONAL DIRICHLET DISTRIBUTIONS 2.2.2 SOME PRELIMINARIES ON
POISSON RANDOM MEASURES 2.2.3 MASS-PARTITIONS INDUCED BY POISSON
MEASURES 2.2.4 GAMMA SUBORDINATORS AND DIRICHLET PROCESSES 2.2.5 STABLE
SUBORDINATORS AND POISSON-DIRICHLET PARTITIONS 2.3 EXCHANGEABLE RANDOM
PARTITIONS 2.3.1 SOME DEFINITION 2.3.2 KINGMAN'S THEORY 2.3.3
EXCHANGEABLE PARTITION PROBABILITY FUNCTIONS 2.4 COMMENTS EXCHANGEABLE
FRAGMENTATIONS 3.1 HOMOGENEOUS FRAGMENTATION PROCESSES 3.1.1
FRAGMENTATION OF PARTITIONS 3.1.2 HOMOGENEOUS FRAGMENTATION AS MARKOV
PROCESSES 3.1.3 POISSONIAN STRUCTURE 3.2 ASYMPTOTIC FREQUENCIES 3.2.1
EROSION AND DISLOCATION 3.2.2 SUBORDINATOR REPRESENTATION OF THE TAGGED
FRAGMENT 3.2.3 LEVY-ITO DECOMPOSITION OF THE TAGGED FRAGMENT 3.3
SELF-SIMILAR FRAGMENTATIONS 3.3.1 DEFINITION AND FIRST PROPERTIES 3.3.2
CHANGING THE INDEX OF SELF-SIMILARITY 3.3.3 MASS-FRAGMENTATIONS 3.4
COMMENTS EXCHANGEABLE COALESCENTS .-- 4.1 KINGMAN'S COALESCENT 4.1.1
GENEALOGY OF POPULATIONS IN THE WRIGHT-FISHER MODEL 4.1.2 CONSTRUCTION
OF KINGMAN'S COALESCENT 4.1.3 INTERVAL REPRESENTATION OF KINGMAN'S
COALESCENT 4.2 SIMULTANEOUS AND MULTIPLE COAGULATIONS 4.2.1 COAGULATION
OF PARTITIONS 4.2.2 EXCHANGEABLE COALESCENTS AND COAGULATION RATES 4.2.3
POISSONIAN CONSTRUCTION 4.2.4 CHARACTERIZATION OF COAGULATION RATES 4.3
EXCHANGEABLE MASS-COALESCENTS 4.3.1 MARKOV PROPERTY 4.3.2 DUST IN
EXCHANGEABLE MASS-COALESCENTS CONTENTS VII 4.4 SIMPLE COALESCENTS AND
FLOWS OF BRIDGES 189 4.4.1 COMPOSITIONS OF SIMPLE BRIDGES 190 4.4.2
FLOWS OF BRIDGES AND COAGULATION 196 4.4.3 THE DUAL FLOW AND A
POPULATION MODEL 200 4.4.4 THE BOLTHAUSEN-SZNITMAN COALESCENT 205 4.5
COMMENTS 211 ASYMPTOTIC REGIMES IN STOCHASTIC COALESCENCE 214 5.1
STOCHASTIC COALESCENCE 214 5.1.1 COALESCENT CHAINS 215 5.1.2 EXTENSION
TO INFINITE SYSTEMS 218 5.2 HYDRODYNAMIC BEHAVIOR AND SMOLUCHOWSKI'S
EQUATIONS 226 5.2.1 THE MULTIPLICATIVE KERNEL 227 5.2.2
SUB-MULTIPLICATIVE KERNELS 235 5.3 THE ADDITIVE COALESCENCE 244 5.3.1
SOME BASIC PROPERTIES 244 5.3.2 COAGULATION OF TREES IN A RANDOM FOREST
247 5.3.3 THE STANDARD ADDITIVE COALESCENT 254 5.3.4 A DUAL
FRAGMENTATION PROCESS 258 5.4 COMMENTS 261 REFERENCES 264 LIST OF
SYMBOLS 276 INDEX 27 9 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T16:41:33Z |
| indexdate | 2024-07-09T20:53:30Z |
| institution | BVB |
| isbn | 0521867282 9780521867283 |
| language | English |
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| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Bertoin, Jean 1961- Verfasser (DE-588)121404455 aut Random fragmentation and coagulation processes Jean Bertoin Cambridge Cambridge University Press 2006 vii, 280 p. ill. 24 cm txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 102 Includes bibliographical references and index Processus stochastiques Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s DE-604 Cambridge studies in advanced mathematics 102 (DE-604)BV000003678 102 http://www.loc.gov/catdir/enhancements/fy0702/2006297175-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0702/2006297175-t.html Table of contents only GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015467948&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bertoin, Jean 1961- Random fragmentation and coagulation processes Cambridge studies in advanced mathematics Processus stochastiques Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 |
| title | Random fragmentation and coagulation processes |
| title_auth | Random fragmentation and coagulation processes |
| title_exact_search | Random fragmentation and coagulation processes |
| title_exact_search_txtP | Random fragmentation and coagulation processes |
| title_full | Random fragmentation and coagulation processes Jean Bertoin |
| title_fullStr | Random fragmentation and coagulation processes Jean Bertoin |
| title_full_unstemmed | Random fragmentation and coagulation processes Jean Bertoin |
| title_short | Random fragmentation and coagulation processes |
| title_sort | random fragmentation and coagulation processes |
| topic | Processus stochastiques Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Processus stochastiques Stochastic processes Stochastischer Prozess |
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