Probability measures on semigroups: convolution products, random walks, and random matrices
This original work presents up-to-date information on three major topics in mathematics research: the theory of weak convergence of convolution products of probability measures in semigroups; the theory of random walks with values in semigroups; and the applications of these theories to products of...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Plenum Press
1995
|
| Schriftenreihe: | The University series in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This original work presents up-to-date information on three major topics in mathematics research: the theory of weak convergence of convolution products of probability measures in semigroups; the theory of random walks with values in semigroups; and the applications of these theories to products of random matrices. The authors introduce the main topics through the fundamentals of abstract semigroup theory and significant research results concerning its application to concrete semigroups of matrices. The material is suitable for a two-semester graduate course on weak convergence and random walks. It is assumed that the student will have a background in Probability Theory, Measure Theory, and Group Theory. |
| Beschreibung: | XII, 388 S. |
| ISBN: | 0306449641 |
Internformat
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Datensatz im Suchindex
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| adam_text | IMAGE 1
PROBABILITY MEASURES
ON SEMIGROUPS CONVOLUTION PRODUCTS, RANDOM WALKS, AND RANDOM MATRICES
GORAN HOGNAS ARUNAVA MUKHERJEA ABO AKADEMI UNIVERSITY UNIVERSITY OF
SOUTH FLORIDA
ABO, FINLAND TAMPA, FLORIDA
PLENUM PRESS * NEW YORK AND LONDON
IMAGE 2
CONTENTS
1. SEMIGROUPS 1
1.1. INTRODUCTION 1
1.2. HOMOMORPHISMS, QUOTIENTS, AND PRODUCTS 5
1.3. SEMIGROUPS WITH ZERO 9
1.4. REES-SUSCHKEWITSCH REPRESENTATION THEOREM 11
1.5. TOPOLOGICAL SEMIGROUPS -. 22
1.6. SEMIGROUPS OF MATRICES 34
1.7. SEMIGROUPS OF INFINITE DIMENSIONAL MATRICES 52
1.8. EMBEDDING SEMIGROUPS IN A GROUP 60
1.9. NOTES AND COMMENTS 62
REFERENCES 63
2. PROBABILITY MEASURES ON TOPOLOGICAL SEMIGROUPS 67
2.1. INTRODUCTION 67
2.2. INVARIANT AND IDEMPOTENT PROBABILITY MEASURES 68
2.3. WEAK CONVERGENCE OF CONVOLUTION PRODUCTS OF PROBABILITY MEASURES 87
2.4. WEAK CONVERGENCE OF CONVOLUTION PRODUCTS OF NONIDENTICAL
PROBABILITY MEASURES 139
2.5. NOTES AND COMMENTS 168
REFERENCES 169
3. RANDOM WALKS ON SEMIGROUPS 173
3.1. INTRODUCTION 173
3.2. DISCRETE SEMIGROUPS 183
3.3. LOCALLY COMPACT GROUPS 202
3.4. COMPACT SEMIGROUPS 227
XI
IMAGE 3
XII CONTENTS
3.5. COMPLETELY SIMPLE SEMIGROUPS 250
3.6. NOTES AND COMMENTS 256
REFERENCES 260
4. RANDOM MATRICES 263
4.1. INTRODUCTION 263
4.2. RECURRENT RANDOM WALKS IN NONNEGATIVE MATRICES 263 4.3. TIGHTNESS
OF PRODUCTS OF I.I.D. RANDOM MATRICES: WEAK CONVERGENCE 292
4.4. INVARIANT MEASURES FOR RANDOM WALKS IN NONNEGATIVE MATRICES: LAWS
OF LARGE NUMBERS 342
4.5. ASYMPTOTIC BEHAVIOR OF X N X N -X.. .XOU FOR I.I.D. RANDOM
NONNEGATIVE MATRICES 365
4.6. NOTES AND COMMENTS 377
REFERENCES 379
INDEX 383
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:03:39Z |
| institution | BVB |
| isbn | 0306449641 |
| language | English |
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| physical | XII, 388 S. |
| publishDate | 1995 |
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| series2 | The University series in mathematics |
| spelling | Högnäs, Göran Verfasser aut Probability measures on semigroups convolution products, random walks, and random matrices Göran Högnäs ; Arunava Mukherjea New York [u.a.] Plenum Press 1995 XII, 388 S. txt rdacontent n rdamedia nc rdacarrier The University series in mathematics This original work presents up-to-date information on three major topics in mathematics research: the theory of weak convergence of convolution products of probability measures in semigroups; the theory of random walks with values in semigroups; and the applications of these theories to products of random matrices. The authors introduce the main topics through the fundamentals of abstract semigroup theory and significant research results concerning its application to concrete semigroups of matrices. The material is suitable for a two-semester graduate course on weak convergence and random walks. It is assumed that the student will have a background in Probability Theory, Measure Theory, and Group Theory. Mesures de probabilités ram Semigroupes ram Probability measures Semigroups Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Halbgruppe (DE-588)4022990-7 gnd rswk-swf Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Halbgruppe (DE-588)4022990-7 s Wahrscheinlichkeitsmaß (DE-588)4137556-7 s Mukherjea, Arunava Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007422434&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Högnäs, Göran Mukherjea, Arunava Probability measures on semigroups convolution products, random walks, and random matrices Mesures de probabilités ram Semigroupes ram Probability measures Semigroups Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Halbgruppe (DE-588)4022990-7 gnd Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4022990-7 (DE-588)4137556-7 |
| title | Probability measures on semigroups convolution products, random walks, and random matrices |
| title_auth | Probability measures on semigroups convolution products, random walks, and random matrices |
| title_exact_search | Probability measures on semigroups convolution products, random walks, and random matrices |
| title_full | Probability measures on semigroups convolution products, random walks, and random matrices Göran Högnäs ; Arunava Mukherjea |
| title_fullStr | Probability measures on semigroups convolution products, random walks, and random matrices Göran Högnäs ; Arunava Mukherjea |
| title_full_unstemmed | Probability measures on semigroups convolution products, random walks, and random matrices Göran Högnäs ; Arunava Mukherjea |
| title_short | Probability measures on semigroups |
| title_sort | probability measures on semigroups convolution products random walks and random matrices |
| title_sub | convolution products, random walks, and random matrices |
| topic | Mesures de probabilités ram Semigroupes ram Probability measures Semigroups Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Halbgruppe (DE-588)4022990-7 gnd Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd |
| topic_facet | Mesures de probabilités Semigroupes Probability measures Semigroups Wahrscheinlichkeitstheorie Halbgruppe Wahrscheinlichkeitsmaß |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007422434&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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