Stochastic differential equations in infinite dimensional spaces: an extended version of the lectures delivered by Gopinath Kallianpur as part of "1993-Barrett Lectures" at the University of Tennessee, Knoxville, TN
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Hayward, Calif.
Inst. of Math. Statistics
1995
|
| Schriftenreihe: | Institute of Mathematical Statistics: Lecture notes, monograph series
26 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007844848&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | VI, 342 S. |
| ISBN: | 0940600382 |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 600f 2001 A 893-26 |
|---|---|
| DE-BY-TUM_katkey | 1499698 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020097298 |
| _version_ | 1821933243370307585 |
| adam_text | INSTITUTE OF MATHEMATICAL STATISTICS LECTURE NOTES - MONOGRAPH SERIES
VOLUME 26 GOPINATH KALLIANPUR DEPARTMENT OF STATISTICS UNIVERSITY OF
NORTH CAROLINA CHAPEL HILL, NC 27599-3260 JIE XIONG DEPARTMENT OF
MATHEMATICS UNIVERSITY OF TENNESSEE KNOXVILLE, TN 37996-1300 STOCHASTIC
DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONAL SPACES (AN EXTENDED
VERSION OF THE LECTURES DELIVERED BY GOPINATH KALLIANPUR AS PART OF
1993-BARRETT LECTURES AT THE UNIVERSITY OF TENNESSEE, KNOXVILLE, TN) SUB
GDTTLNGEN 7 208 589 260 98 A 21343 V ORGANIZERS OF 1993-BARRETT
LECTURES: BALRAM RAJPUT^AND JAN ROSINSKI -INSTITUTE OF MATHEMATICAL
STATISTICS HAYWARD, CALIFORNIA CONTENTS FOREWORD I PREFACE III 1
TOPOLOGICAL VECTOR SPACES 1 1.1 TOPOLOGICAL VECTOR SPACES 1 1.2 LINEAR
OPERATORS 16 1.3 COUNTABLY HILBERTIAN NUCLEAR SPACES 29 2 PROBABILITY
MEASURES 45 2.1 PROBABILITY MEASURES 45 2.2 WEAK CONVERGENCE OF
PROBABILITY MEASURES 55 2.3 MINLOS AND SAZONOV THEOREMS 61 2.4
C([0,T],$ ) AND.D([0,T],* ) 71 2.5 PROBABILITY MEASURES ON D([0,T],$ / )
. 80 3 STOCHASTIC INTEGRALS 85 3.1 MARTINGALES 86 3.2 3 -WIENER PROCESS
93 3.3 CONTINUOUS STOCHASTIC INTEGRAL 109 3.3.1 STOCHASTIC INTEGRAL 109
3.3.2 REPRESENTATION THEOREMS 113 3.4 DISCONTINUOUS STOCHASTIC INTEGRAL
119 4 SPDE 127 4.1 INTRODUCTION 127 4.2 SPACE-TIME ORNSTEIN-UHLENBECK
SDE 129 4.3 SPDES 134 4.4 NONLINEAR STOCHASTIC CABLE EQUATION 141 4.5
O-U SDE S DRIVEN BY POISSON RANDOM MEASURES 144 VI CONTENTS 5 SDE IN
HILBERT SPACE 149 5.1 DIFFUSION EQUATIONS IN HILBERT SPACES 149 5.2
STOCHASTIC EVOLUTION EQUATIONS 154 6 STOCHASTIC DIFFERENTIAL EQUATIONS
171 6.1 WEAK CONVERGENCE THEOREMS 172 6.2 EXISTENCE OF A WEAK SOLUTION
189 6.3 STRONG SOLUTION 199 7 ENVIRONMENTAL POLLUTION 211 7.1
INTRODUCTION 211 7.2 POLLUTION WITH POISSON DEPOSITS 213 7.3 POLLUTION
ALONG A RIVER 221 7.4 POLLUTION WITH A TOLERANCE LEVEL 229 7.5 FILTERING
PROBLEM 230 8 DIFFUSION PROCESSES 239 8.1 MARTINGALE PROBLEM OF A
DIFFUSION EQUATION 240 8.2 WEAK SOLUTIONS OF DIFFUSION EQUATIONS 248 8.3
STRONG SOLUTION OF DIFFUSION EQUATION 253 8.4 APPLICATIONS OF DIFFUSION
APPROXIMATION 260 8.5 EXAMPLES OF NUCLEAR-SPACE-VALUED SDE S 273 9
INTERACTING SYSTEMS 279 9.1 MCKEAN-VLASOV EQUATION 280 9.2 INTERACTING
SYSTEMS 284 10 LARGE DEVIATIONS 299 10.1 LDP FOR A CLASS OF RANDOM
VARIABLES 299 10.2 APPLICATION TO SDE IN CONUCLEAR SPACE 308 10.3
APPLICATION TO SPDES 320 10.4 REACTION-DIFFUSION SPDES 331 BIBLIOGRAPHY
335 INDEX 340
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| discipline | Mathematik |
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| id | DE-604.BV011640466 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:16:07Z |
| institution | BVB |
| isbn | 0940600382 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007844848 |
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| physical | VI, 342 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Inst. of Math. Statistics |
| record_format | marc |
| series | Institute of Mathematical Statistics: Lecture notes, monograph series |
| series2 | Institute of Mathematical Statistics: Lecture notes, monograph series |
| spellingShingle | Kallianpur, Gopinath 1925- Xiong, Jie Stochastic differential equations in infinite dimensional spaces an extended version of the lectures delivered by Gopinath Kallianpur as part of "1993-Barrett Lectures" at the University of Tennessee, Knoxville, TN Institute of Mathematical Statistics: Lecture notes, monograph series Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4057621-8 (DE-588)1071861417 |
| title | Stochastic differential equations in infinite dimensional spaces an extended version of the lectures delivered by Gopinath Kallianpur as part of "1993-Barrett Lectures" at the University of Tennessee, Knoxville, TN |
| title_auth | Stochastic differential equations in infinite dimensional spaces an extended version of the lectures delivered by Gopinath Kallianpur as part of "1993-Barrett Lectures" at the University of Tennessee, Knoxville, TN |
| title_exact_search | Stochastic differential equations in infinite dimensional spaces an extended version of the lectures delivered by Gopinath Kallianpur as part of "1993-Barrett Lectures" at the University of Tennessee, Knoxville, TN |
| title_full | Stochastic differential equations in infinite dimensional spaces an extended version of the lectures delivered by Gopinath Kallianpur as part of "1993-Barrett Lectures" at the University of Tennessee, Knoxville, TN Gopinath Kallianpur ; Jie Xiong |
| title_fullStr | Stochastic differential equations in infinite dimensional spaces an extended version of the lectures delivered by Gopinath Kallianpur as part of "1993-Barrett Lectures" at the University of Tennessee, Knoxville, TN Gopinath Kallianpur ; Jie Xiong |
| title_full_unstemmed | Stochastic differential equations in infinite dimensional spaces an extended version of the lectures delivered by Gopinath Kallianpur as part of "1993-Barrett Lectures" at the University of Tennessee, Knoxville, TN Gopinath Kallianpur ; Jie Xiong |
| title_short | Stochastic differential equations in infinite dimensional spaces |
| title_sort | stochastic differential equations in infinite dimensional spaces an extended version of the lectures delivered by gopinath kallianpur as part of 1993 barrett lectures at the university of tennessee knoxville tn |
| title_sub | an extended version of the lectures delivered by Gopinath Kallianpur as part of "1993-Barrett Lectures" at the University of Tennessee, Knoxville, TN |
| topic | Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Stochastische Differentialgleichung Konferenzschrift Unendlich dimensionaler Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007844848&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008930051 |
| work_keys_str_mv | AT kallianpurgopinath stochasticdifferentialequationsininfinitedimensionalspacesanextendedversionofthelecturesdeliveredbygopinathkallianpuraspartof1993barrettlecturesattheuniversityoftennesseeknoxvilletn AT xiongjie stochasticdifferentialequationsininfinitedimensionalspacesanextendedversionofthelecturesdeliveredbygopinathkallianpuraspartof1993barrettlecturesattheuniversityoftennesseeknoxvilletn |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 600f 2001 A 893-26
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |