Stability of infinite dimensional stochastic differential equations with applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2006
|
| Series: | Chapman & Hall CRC Monographs and Surveys in Pure and Applied Mathematics
135 |
| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 273 - 295 |
| Physical Description: | XI, 298 S. 24 cm |
| ISBN: | 158488598X 9781584885986 |
Staff View
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Record in the Search Index
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| adam_text | CONTENTS PREFACE I X 1 STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE
DIMENSIONS 1 1.1 NOTATIONS, DEFINITIONS AND PRELIMINARIES 1 1.2 WIENER
PROCESSES AND STOCHASTIC INTEGRATION 11 1.3 STOCHASTIC EVOLUTION
EQUATIONS 16 1.3.1 VARIATIONAL APPROACH AND STRONG SOLUTIONS 18 1.3.2
SEMIGROUP APPROACH AND MILD SOLUTIONS 22 1.4 DEFINITIONS AND METHODS OF
STABILITY 29 1.5 NOTES AND COMMENTS 37 2 STABILITY OF LINEAR STOCHASTIC
DIFFERENTIAL EQUATIONS 39 2.1 STAHLE SEMIGROUPS 39 2.1.1 LYAPUNOV
FUNCTIONS 42 2.1.2 A USEFUL STABILITY CRITERION 51 2.2 LYAPUNOV
EQUATIONS AND STABILITY 54 2.2.1 CHARACTERIZATION OF MEAN SQUARE
STABILITY 55 2.2.2 ALMOST SURE PATHWISE STABILITY 63 2.3 UNIFORMLY
ASYMPTOTIC STABILITY 70 2.4 SOME EXAMPLES 73 2.5 NOTES AND COMMENTS 78 3
STABILITY OF NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS 81 3.1
EQUIVALENCE OF L P -STABILITY AND EXPONENTIAL STABILITY . . . . 81 3.1.1
AN EXTENSION OF LINEAR STABILITY CRITERIA 83 3.1.2 COMPARISON APPROACHES
88 3.2 A COERCIVE DECAY CONDITION 94 3.3 STABILITY OF SEMILINEAR
STOCHASTIC EVOLUTION EQUATIONS . . . . 102 3.4 LYAPUNOV FUNCTIONS FOR
STRONG SOLUTIONS 110 3.5 TWO APPLICATIONS 121 3.5.1 STABILITY IN
PROBABILITY 121 3.5.2 ULTIMATE BOUNDEDNESS AND INVARIANT MEASURES . . .
. 124 3.6 FURTHER RESULTS ON INVARIANT MEASURES 131 3.7 STABILITY,
ULTIMATE BOUNDEDNESS OF MILD SOLUTIONS AND INVARI- ANT MEASURES 137
3.7.1 LYAPUNOV FUNCTIONS FOR MILD SOLUTIONS 137 3.7.2 ULTIMATE
BOUNDEDNESS AND INVARIANT MEASURES . . . . 143 VN VLLL CONTENTS 3.8
DECAY RATES OF SYSTEMS 150 3.8.1 DECAY IN THE P-TH MOMENT 151 3.8.2
ALMOST SURE PATHWISE DECAY 154 3.9 STABILIZATION OF SYSTEMS BY NOISE 159
3.9.1 NONLINEAR DETERMINISTIC EQUATIONS 160 3.9.2 NONLINEAR STOCHASTIC
EQUATIONS 164 3.10 LYAPUNOV EXPONENTS AND STABILIZATION 166 3.11 NOTES
AND COMMENTS 173 4 STABILITY OF STOCHASTIC FUNCTIONAL DIFFERENTIAL
EQUATIONS 175 4.1 LINEAR DETERMINISTIC EQUATIONS 175 4.1.1 STABLE
SEMIGROUPS (FINITE DELAYS) 176 4.1.2 STABLE SEMIGROUPS (INFINITE DELAYS)
186 4.2 STABILITY EQUIVALENCE AND REDUCTION OF NEUTRAL EQUATIONS . 192
4.2.1 STABILITY OF RETARDED STOCHASTIC SYSTEMS 192 4.2.2 STABILITY OF
NEUTRAL STOCHASTIC SYSTEMS 201 4.3 DECAY CRITERIA OF STOCHASTIC DELAY
DIFFERENTIAL EQUATIONS . . 212 4.3.1 NONLINEAR COERCIVE CONDITIONS FOR
DECAY 213 4.3.2 LINEAR STABILITY CONDITIONS 217 4.4 RAZUMIKHIN TYPE
STABILITY THEOREMS 220 4.5 NOTES AND COMMENTS 227 5 SOME RELATED TOPICS
OF STABILITY AND APPLICATIONS 229 5.1 PARABOLIC EQUATIONS WITH BOUNDARY
AND POINTWISE NOISE . . 229 5.2 STOCHASTIC STABILITY AND QUADRATIC
CONTROL 236 5.2.1 OPTIMAL CONTROL ON A FINITE INTERVAL 237 5.2.2 OPTIMAL
CONTROL ON AN INFINITE INTERVAL 241 5.3 FEEDBACK STABILIZATION OF
STOCHASTIC DIFFERENTIAL EQUATIONS . 246 5.4 STOCHASTIC MODELS IN
MATHEMATICAL PHYSICS 251 5.4.1 STOCHASTIC REACTION-DIFFUSION EQUATIONS
251 5.4.2 STOCHASTIC NAVIER-STOKES EQUATIONS 254 5.5 STOCHASTIC SYSTEMS
RELATED TO MULTI-SPECIES POPULATION DY- NAMICS 257 5.6 NOTES AND
COMMENTS 264 APPENDIX 267 A THE PROOF OF PROPOSITION 4.2.4 267 B
EXISTENCE AND UNIQUENESS OF STRENG SOLUTIONS OF STOCHASTIC DE- LAY
DIFFERENTIAL EQUATIONS 268 REFERENCES 273 INDEX 297
|
| adam_txt |
CONTENTS PREFACE I X 1 STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE
DIMENSIONS 1 1.1 NOTATIONS, DEFINITIONS AND PRELIMINARIES 1 1.2 WIENER
PROCESSES AND STOCHASTIC INTEGRATION 11 1.3 STOCHASTIC EVOLUTION
EQUATIONS 16 1.3.1 VARIATIONAL APPROACH AND STRONG SOLUTIONS 18 1.3.2
SEMIGROUP APPROACH AND MILD SOLUTIONS 22 1.4 DEFINITIONS AND METHODS OF
STABILITY 29 1.5 NOTES AND COMMENTS 37 2 STABILITY OF LINEAR STOCHASTIC
DIFFERENTIAL EQUATIONS 39 2.1 STAHLE SEMIGROUPS 39 2.1.1 LYAPUNOV
FUNCTIONS 42 2.1.2 A USEFUL STABILITY CRITERION 51 2.2 LYAPUNOV
EQUATIONS AND STABILITY 54 2.2.1 CHARACTERIZATION OF MEAN SQUARE
STABILITY 55 2.2.2 ALMOST SURE PATHWISE STABILITY 63 2.3 UNIFORMLY
ASYMPTOTIC STABILITY 70 2.4 SOME EXAMPLES 73 2.5 NOTES AND COMMENTS 78 3
STABILITY OF NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS 81 3.1
EQUIVALENCE OF L P -STABILITY AND EXPONENTIAL STABILITY . . . . 81 3.1.1
AN EXTENSION OF LINEAR STABILITY CRITERIA 83 3.1.2 COMPARISON APPROACHES
88 3.2 A COERCIVE DECAY CONDITION 94 3.3 STABILITY OF SEMILINEAR
STOCHASTIC EVOLUTION EQUATIONS . . . . 102 3.4 LYAPUNOV FUNCTIONS FOR
STRONG SOLUTIONS 110 3.5 TWO APPLICATIONS 121 3.5.1 STABILITY IN
PROBABILITY 121 3.5.2 ULTIMATE BOUNDEDNESS AND INVARIANT MEASURES . . .
. 124 3.6 FURTHER RESULTS ON INVARIANT MEASURES 131 3.7 STABILITY,
ULTIMATE BOUNDEDNESS OF MILD SOLUTIONS AND INVARI- ANT MEASURES 137
3.7.1 LYAPUNOV FUNCTIONS FOR MILD SOLUTIONS 137 3.7.2 ULTIMATE
BOUNDEDNESS AND INVARIANT MEASURES . . . . 143 VN VLLL CONTENTS 3.8
DECAY RATES OF SYSTEMS 150 3.8.1 DECAY IN THE P-TH MOMENT 151 3.8.2
ALMOST SURE PATHWISE DECAY 154 3.9 STABILIZATION OF SYSTEMS BY NOISE 159
3.9.1 NONLINEAR DETERMINISTIC EQUATIONS 160 3.9.2 NONLINEAR STOCHASTIC
EQUATIONS 164 3.10 LYAPUNOV EXPONENTS AND STABILIZATION 166 3.11 NOTES
AND COMMENTS 173 4 STABILITY OF STOCHASTIC FUNCTIONAL DIFFERENTIAL
EQUATIONS 175 4.1 LINEAR DETERMINISTIC EQUATIONS 175 4.1.1 STABLE
SEMIGROUPS (FINITE DELAYS) 176 4.1.2 STABLE SEMIGROUPS (INFINITE DELAYS)
186 4.2 STABILITY EQUIVALENCE AND REDUCTION OF NEUTRAL EQUATIONS . 192
4.2.1 STABILITY OF RETARDED STOCHASTIC SYSTEMS 192 4.2.2 STABILITY OF
NEUTRAL STOCHASTIC SYSTEMS 201 4.3 DECAY CRITERIA OF STOCHASTIC DELAY
DIFFERENTIAL EQUATIONS . . 212 4.3.1 NONLINEAR COERCIVE CONDITIONS FOR
DECAY 213 4.3.2 LINEAR STABILITY CONDITIONS 217 4.4 RAZUMIKHIN TYPE
STABILITY THEOREMS 220 4.5 NOTES AND COMMENTS 227 5 SOME RELATED TOPICS
OF STABILITY AND APPLICATIONS 229 5.1 PARABOLIC EQUATIONS WITH BOUNDARY
AND POINTWISE NOISE . . 229 5.2 STOCHASTIC STABILITY AND QUADRATIC
CONTROL 236 5.2.1 OPTIMAL CONTROL ON A FINITE INTERVAL 237 5.2.2 OPTIMAL
CONTROL ON AN INFINITE INTERVAL 241 5.3 FEEDBACK STABILIZATION OF
STOCHASTIC DIFFERENTIAL EQUATIONS . 246 5.4 STOCHASTIC MODELS IN
MATHEMATICAL PHYSICS 251 5.4.1 STOCHASTIC REACTION-DIFFUSION EQUATIONS
251 5.4.2 STOCHASTIC NAVIER-STOKES EQUATIONS 254 5.5 STOCHASTIC SYSTEMS
RELATED TO MULTI-SPECIES POPULATION DY- NAMICS 257 5.6 NOTES AND
COMMENTS 264 APPENDIX 267 A THE PROOF OF PROPOSITION 4.2.4 267 B
EXISTENCE AND UNIQUENESS OF STRENG SOLUTIONS OF STOCHASTIC DE- LAY
DIFFERENTIAL EQUATIONS 268 REFERENCES 273 INDEX 297 |
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| id | DE-604.BV035005012 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:41:50Z |
| indexdate | 2024-07-09T21:20:00Z |
| institution | BVB |
| isbn | 158488598X 9781584885986 |
| language | English |
| lccn | 2005049377 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016674342 |
| oclc_num | 60590157 |
| open_access_boolean | |
| owner | DE-384 DE-83 |
| owner_facet | DE-384 DE-83 |
| physical | XI, 298 S. 24 cm |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Chapman & Hall CRC Monographs and Surveys in Pure and Applied Mathematics |
| series2 | Chapman & Hall CRC Monographs and Surveys in Pure and Applied Mathematics |
| spelling | Liu, Kai Verfasser aut Stability of infinite dimensional stochastic differential equations with applications Kai Liu Boca Raton [u.a.] Chapman & Hall/CRC 2006 XI, 298 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Chapman & Hall CRC Monographs and Surveys in Pure and Applied Mathematics 135 Literaturverz. S. 273 - 295 Variétés de dimension infinie Équations différentielles stochastiques Stochastic differential equations Infinite-dimensional manifolds Stabilität (DE-588)4056693-6 gnd rswk-swf Dimension unendlich (DE-588)4474010-4 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Stabilität (DE-588)4056693-6 s Stochastische Differentialgleichung (DE-588)4057621-8 s Dimension unendlich (DE-588)4474010-4 s DE-604 Chapman & Hall CRC Monographs and Surveys in Pure and Applied Mathematics 135 (DE-604)BV013350872 135 http://www.loc.gov/catdir/enhancements/fy0653/2005049377-d.html Publisher description GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016674342&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Liu, Kai Stability of infinite dimensional stochastic differential equations with applications Chapman & Hall CRC Monographs and Surveys in Pure and Applied Mathematics Variétés de dimension infinie Équations différentielles stochastiques Stochastic differential equations Infinite-dimensional manifolds Stabilität (DE-588)4056693-6 gnd Dimension unendlich (DE-588)4474010-4 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4056693-6 (DE-588)4474010-4 (DE-588)4057621-8 |
| title | Stability of infinite dimensional stochastic differential equations with applications |
| title_auth | Stability of infinite dimensional stochastic differential equations with applications |
| title_exact_search | Stability of infinite dimensional stochastic differential equations with applications |
| title_exact_search_txtP | Stability of infinite dimensional stochastic differential equations with applications |
| title_full | Stability of infinite dimensional stochastic differential equations with applications Kai Liu |
| title_fullStr | Stability of infinite dimensional stochastic differential equations with applications Kai Liu |
| title_full_unstemmed | Stability of infinite dimensional stochastic differential equations with applications Kai Liu |
| title_short | Stability of infinite dimensional stochastic differential equations with applications |
| title_sort | stability of infinite dimensional stochastic differential equations with applications |
| topic | Variétés de dimension infinie Équations différentielles stochastiques Stochastic differential equations Infinite-dimensional manifolds Stabilität (DE-588)4056693-6 gnd Dimension unendlich (DE-588)4474010-4 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Variétés de dimension infinie Équations différentielles stochastiques Stochastic differential equations Infinite-dimensional manifolds Stabilität Dimension unendlich Stochastische Differentialgleichung |
| url | http://www.loc.gov/catdir/enhancements/fy0653/2005049377-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016674342&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013350872 |
| work_keys_str_mv | AT liukai stabilityofinfinitedimensionalstochasticdifferentialequationswithapplications |