Stochastic partial differential equations with Lévy noise: an evolution equation approach
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Edition: | 1. publ. |
| Series: | Encyclopedia of mathematics and its applications
113 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 403 - 414 |
| Physical Description: | XII, 419 S. |
| ISBN: | 9780521879897 |
Staff View
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| 245 | 1 | 0 | |a Stochastic partial differential equations with Lévy noise |b an evolution equation approach |c S. Peszat and J. Zabczyk, Institute of Mathematics, Polish Academy of Sciences |
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Record in the Search Index
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| adam_text | STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH LEVY NOISE AN EVOLUTION
EQUATION APPROACH S..PESZAT AND J. ZABCZYK INSTITUTE OF MATHEMATICS,
POLISH ACADEMY OF SCIENCES CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE
PAGE IX PARTI FOUNDATIONS 1 1 WHY EQUATIONS WITH LEVY NOISE? 3 1.1
DISCRETE-TIME DYNAMICAL SYSTEMS 3 1.2 DETERMINISTIC CONTINUOUS-TIME
SYSTEMS 5 1.3 STOCHASTIC CONTINUOUS-TIME SYSTEMS 6 1.4 COURREGE S
THEOREM 8 1.5 ITO S APPROACH 9 1.6 INFINITE-DIMENSIONAL CASE 12 2
ANALYTIC PRELIMINARIES 13 2.1 NOTATION 13 2.2 SOBOLEV AND HOLDER
SPACES 13 2.3 L P - AND C P -SPACES 15 2.4 LIPSCHITZ FUNCTIONS AND
COMPOSITION OPERATORS 16 2.5 DIFFERENTIAL OPERATORS 17 3 PROBABILISTIC
PRELIMINARIES 20 3.1 BASIC DEFINITIONS ~ 20 3.2 KOLMOGOROV EXISTENCE
THEOREM 22 3.3 RANDOM ELEMENTS IN BANACTI SPACES 23 3.4 STOCHASTIC
PROCESSES IN BANACH SPACES 25 3.5 GAUSSIAN MEASURES ON HILBERT SPACES 28
3.6 GAUSSIAN 1 MEASURES ON TOPOLOGICAL SPACES 30 3.7 SUBMARTINGALES ,
; * . 31 3.8 SEMIMARTINGALES * 36 3.9 BURKHOLDER-DAVIES-GUHDY
INEQUALITIES . 37 VI CONTENTS 4 LEVY PROCESSES 38 4.1 BASIC PROPERTIES
38 4.2 TWO BUILDING BLOCKS - POISSON AND WIENER PROCESSES 40 4.3
COMPOUND POISSON PROCESSES IN A HILBERT SPACE 45 4.4 WIENER PROCESSES IN
A HILBERT SPACE 50 4.5 LEVY-KHINCHIN DECOMPOSITION 52 4.6 LEVY-KHINCHIN
FORMULA 56 4.7 LAPLACE TRANSFORMS OF CONVOLUTION SEMIGROUPS 57 4.8
EXPANSION WITH RESPECT TO AN ORTHONORMAL BASIS 62 4.9 SQUARE INTEGRABLE
LEVY PROCESSES 65 4.10 LEVY PROCESSES ON BANACH SPACES 72 5 LEVY
SEMIGROUPS 75 5.1 BASIC PROPERTIES 75 5.2 GENERATORS 78 6 POISSON
RANDOM MEASURES 83 6.1 INTRODUCTION . 83 6.2 STOCHASTIC INTEGRAL OF
DETERMINISTIC FIELDS 85 6.3 APPLICATION TO CONSTRUCTION OF LEVY
PROCESSES . 87 6.4 MOMENT ESTIMATES IN BANACH SPACES 90 7 CYLINDRICAL
PROCESSES AND REPRODUCING KERNELS 91 7.1 REPRODUCING KERNEL HILBERT
SPACE 91 7.2 CYLINDRICAL POISSON PROCESSES _ , 100 7.3 COMPENSATED
POISSON MEASURE AS A MARTINGALE . 105 8 STOCHASTIC INTEGRATION 107 8.1
OPERATOR-VALUED ANGLE BRACKET PROCESS ; . - 107 8.2 CONSTRUCTION OF THE
STOCHASTIC INTEGRAL -111 8.3 SPACE OF INTEGRANDS 114 8.4 LOCAL
PROPERTIES OF STOCHASTIC INTEGRALS , . 117 8.5 STOCHASTIC FUBINI THEOREM
,118 8.6 STOCHASTIC INTEGRAL WITH RESPECT TO A LEVY PROCESS , 121 8.7
INTEGRATION WITH RESPECT TO A POISSON RANDOM MEASURE 125 8.8 L P -THEORY
FOR VECTOR-VALUED INTEGRANDS 130 PART II EXISTENCE AND REGULARITY .137
9. GENERAL EXISTENCE AND,UNIQUENESS RESULTS 139 9.1 DETERMINISTIC LINEAR
EQUATIONS 139 9.2 MILD SOLUTIONS -. 141 9.3 EQUIVALENCE OF WEAK AND
MILD SOLUTIONS * . . 148 9.4 LINEAR EQUATIONS 155 CONTENTS VII 9.5
EXISTENCE OF WEAK SOLUTIONS *. 164 9.6 MARKOV PROPERTY X 167 9.7
EQUATIONS WITH GENERAL LEVY PROCESSES 170 9.8 GENERATORS AND A
MARTINGALE PROBLEM 174 10 EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS 179
10.1 DISSIPATIVE MAPPINGS 179 . 10.2 EXISTENCE THEOREM 183 10.3
REACTION-DIFFUSION EQUATION 187 11 FACTORIZATION AND REGULARITY 190 11.1
FINITE-DIMENSIONAL CASE 190 11.2 INFINITE-DIMENSIONAL CASE 193 11.3
APPLICATIONS TO TIME CONTINUITY 197 11.4 THE CASE OF AN ARBITRARY
MARTINGALE 199 12 STOCHASTIC PARABOLIC PROBLEMS 201 12.1 INTRODUCTION
201 12.2 SPACE-TIME CONTINUITY IN THE WIENER CASE 208 12.3 THE JUMP CASE
214 12.4 STOCHASTIC HEAT EQUATION 219 12.5 EQUATIONS WITH FRACTIONAL
LAPLACIAN AND STABLE NOISE 223 13 WAVE AND DELAY EQUATIONS 225 13.1
STOCHASTIC WAVE EQUATION ON [0, 1] 225 13.2 STOCHASTIC WAVE EQUATION ON
M. D DRIVEN BY IMPULSIVE NOISE 230 13.3 STOCHASTIC DELAY EQUATIONS 238
14 EQUATIONS DRIVEN BY A SPATIALLY HOMOGENEOUS NOISE 240 14.1 TEMPERED
DISTRIBUTIONS 240 14.2 LEVY PROCESSES IN S (R D ) 241 14.3 RKHS OF A
SQUARE INTEGRABLE LEVY PROCESS IN S (R D ) 242 14.4 SPATIALLY
HOMOGENEOUS LEVY PROCESSES 246 14.5 EXAMPLES 248 14.6 RKHS OF A
HOMOGENEOUS NOISE 253 14.7 STOCHASTIC EQUATIONS ON R D 255 14.8
STOCHASTIC HEAT EQUATION . 256 14.9 SPACE-TIME REGULARITY IN THE WIENER
CASE 261 14.10 STOCHASTIC WAVE EQUATION 267 15 EQUATIONS WITH NOISE ON
THE BOUNDARY 272 15.1 INTRODUCTION 272 15.2 WEAK AND MILD SOLUTIONS 275
15.3 ANALYTICAL PRELIMINARIES 277 15.4 L 2 CASE 279 15.5 POISSON
PERTURBATION 282 VIII CONTENTS PART III APPLICATIONS 285 16 INVARIANT
MEASURES 287 16.1 BASIC DEFINITIONS 287 16.2 EXISTENCE RESULTS 289 16.3
INVARIANT MEASURES FOR THE REACTION-DIFFUSION EQUATION 297 17 LATTICE
SYSTEMS 299 17.1 INTRODUCTION 299 17.2 GLOBAL INTERACTIONS 300 17.3
REGULAR CASE 303 17.4 NON-LIPSCHITZ CASE 305 17.5 KOLMOGOROV S FORMULA
306 17.6 GIBBS MEASURES 307 18 STOCHASTIC BURGERS EQUATION 312 18.1
BURGERS SYSTEM 312 18.2 UNIQUENESS AND LOCAL EXISTENCE OF SOLUTIONS 314
18.3 STOCHASTIC BURGERS EQUATION WITH ADDITIVE NOISE 317 19
ENVIRONMENTAL POLLUTION MODEL 322 19.1 MODEL 322 20 BOND MARKET MODELS
324 20.1 FORWARD CURVES AND THE HJM POSTULATE * 324 20.2 HJM
CONDITION 327 20.3 HJMM EQUATION 332 20.4 LINEAR VOLATILITY . ^ 20.5 BGM
EQUATION 347 20.6 CONSISTENCY PROBLEM , 350 APPENDIX A OPERATORS OH
HILBERT SPACES 355 APPENDIX B CO-SEMIGROUPS 365 APPENDIX C
REGULARIZATION OF MARKOV PROCESSES 388 APPENDIX D LTD FORMULAE 391
APPENDIX E LEVY-KHINCHIN FORMULA ON [0 , +OO) 394 APPENDIX F PROOF OF
LEMMA 4.24 396 LIST OF SYMBOLS 399 REFERENCES 403 INDEX 415
|
| adam_txt |
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH LEVY NOISE AN EVOLUTION
EQUATION APPROACH S.PESZAT AND J. ZABCZYK INSTITUTE OF MATHEMATICS,
POLISH ACADEMY OF SCIENCES' CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE
PAGE IX PARTI FOUNDATIONS 1 1 WHY EQUATIONS WITH LEVY NOISE? 3 1.1
DISCRETE-TIME DYNAMICAL SYSTEMS 3 1.2 DETERMINISTIC CONTINUOUS-TIME
SYSTEMS ' ' ' 5 1.3 STOCHASTIC CONTINUOUS-TIME SYSTEMS 6 1.4 COURREGE'S
THEOREM 8 1.5 ITO'S APPROACH 9 1.6 INFINITE-DIMENSIONAL CASE 12 2
ANALYTIC PRELIMINARIES 13 2.1 NOTATION ' 13 2.2 SOBOLEV AND HOLDER
SPACES 13 2.3 L P - AND C P -SPACES " ' ' 15 2.4 LIPSCHITZ FUNCTIONS AND
COMPOSITION OPERATORS 16 2.5 DIFFERENTIAL OPERATORS 17 3 PROBABILISTIC
PRELIMINARIES 20 "3.1 BASIC DEFINITIONS ~ 20 3.2 KOLMOGOROV EXISTENCE
THEOREM 22 3.3 RANDOM ELEMENTS IN BANACTI SPACES 23 3.4 STOCHASTIC
PROCESSES IN BANACH SPACES 25 3.5 GAUSSIAN MEASURES ON HILBERT SPACES 28
3.6 GAUSSIAN 1 MEASURES ON TOPOLOGICAL SPACES 30 ' 3.7 SUBMARTINGALES ,
; * . 31 3.8 SEMIMARTINGALES * 36 3.9 BURKHOLDER-DAVIES-GUHDY
INEQUALITIES . 37 VI CONTENTS 4 LEVY PROCESSES 38 4.1 BASIC PROPERTIES
38 4.2 TWO BUILDING BLOCKS - POISSON AND WIENER PROCESSES 40 4.3
COMPOUND POISSON PROCESSES IN A HILBERT SPACE 45 4.4 WIENER PROCESSES IN
A HILBERT SPACE 50 4.5 LEVY-KHINCHIN DECOMPOSITION 52 4.6 LEVY-KHINCHIN
FORMULA 56 4.7 LAPLACE TRANSFORMS OF CONVOLUTION SEMIGROUPS 57 4.8
EXPANSION WITH RESPECT TO AN ORTHONORMAL BASIS 62 4.9 SQUARE INTEGRABLE
LEVY PROCESSES 65 4.10 LEVY PROCESSES ON BANACH SPACES 72 5 LEVY
SEMIGROUPS 75 5.1 BASIC PROPERTIES ' 75 5.2 GENERATORS 78 6 POISSON
RANDOM MEASURES 83 6.1 INTRODUCTION . 83 6.2 STOCHASTIC INTEGRAL OF
DETERMINISTIC FIELDS 85 6.3 APPLICATION TO CONSTRUCTION OF LEVY
PROCESSES . 87 6.4 MOMENT ESTIMATES IN BANACH SPACES 90 7 CYLINDRICAL
PROCESSES AND REPRODUCING KERNELS 91 7.1 REPRODUCING KERNEL HILBERT
SPACE 91 7.2 CYLINDRICAL POISSON PROCESSES _ , 100 7.3 COMPENSATED
POISSON MEASURE AS A MARTINGALE . 105 8 STOCHASTIC INTEGRATION 107 8.1
OPERATOR-VALUED ANGLE BRACKET PROCESS ; . - 107 8.2 CONSTRUCTION OF THE
STOCHASTIC INTEGRAL -111 8.3 SPACE OF INTEGRANDS 114 8.4 LOCAL
PROPERTIES OF STOCHASTIC INTEGRALS , . 117 8.5 STOCHASTIC FUBINI THEOREM
' ,118 8.6 STOCHASTIC INTEGRAL WITH RESPECT TO A LEVY PROCESS , 121 8.7
INTEGRATION WITH RESPECT TO A POISSON RANDOM MEASURE 125 8.8 L P -THEORY
FOR VECTOR-VALUED INTEGRANDS 130 PART II EXISTENCE AND REGULARITY .137
9. GENERAL EXISTENCE AND,UNIQUENESS RESULTS 139 9.1 DETERMINISTIC LINEAR
EQUATIONS '139 9.2 MILD SOLUTIONS \-. 141 9.3 EQUIVALENCE OF WEAK AND
MILD SOLUTIONS * . . 148 9.4 LINEAR EQUATIONS 155 CONTENTS VII 9.5
EXISTENCE OF WEAK SOLUTIONS *. 164 9.6 MARKOV PROPERTY X 167 9.7
EQUATIONS WITH GENERAL LEVY PROCESSES 170 9.8 GENERATORS AND A
MARTINGALE PROBLEM 174 10 EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS 179
10.1 DISSIPATIVE MAPPINGS 179 . 10.2 EXISTENCE THEOREM 183 10.3
REACTION-DIFFUSION EQUATION 187 11 FACTORIZATION AND REGULARITY 190 11.1
FINITE-DIMENSIONAL CASE 190 11.2 INFINITE-DIMENSIONAL CASE 193 11.3
APPLICATIONS TO TIME CONTINUITY 197 11.4 THE CASE OF AN ARBITRARY
MARTINGALE 199 12 STOCHASTIC PARABOLIC PROBLEMS 201 12.1 INTRODUCTION
201 12.2 SPACE-TIME CONTINUITY IN THE WIENER CASE 208 12.3 THE JUMP CASE
214 12.4 STOCHASTIC HEAT EQUATION 219 12.5 EQUATIONS WITH FRACTIONAL
LAPLACIAN AND STABLE NOISE 223 13 WAVE AND DELAY EQUATIONS 225 13.1
STOCHASTIC WAVE EQUATION ON [0, 1] 225 13.2 STOCHASTIC WAVE EQUATION ON
M. D DRIVEN BY IMPULSIVE NOISE 230 13.3 STOCHASTIC DELAY EQUATIONS 238
14 EQUATIONS DRIVEN BY A SPATIALLY HOMOGENEOUS NOISE 240 14.1 TEMPERED
DISTRIBUTIONS 240 14.2 LEVY PROCESSES IN S'(R D ) 241 14.3 RKHS OF A
SQUARE INTEGRABLE LEVY PROCESS IN S'(R D ) 242 14.4 SPATIALLY
HOMOGENEOUS LEVY PROCESSES 246 14.5 EXAMPLES 248 14.6 RKHS OF A
HOMOGENEOUS NOISE 253 14.7 STOCHASTIC EQUATIONS ON R D 255 14.8
STOCHASTIC HEAT EQUATION . 256 14.9 SPACE-TIME REGULARITY IN THE WIENER
CASE 261 14.10 STOCHASTIC WAVE EQUATION 267 15 EQUATIONS WITH NOISE ON
THE BOUNDARY 272 15.1 INTRODUCTION 272 15.2 WEAK AND MILD SOLUTIONS 275
15.3 ANALYTICAL PRELIMINARIES 277 15.4 L 2 CASE 279 15.5 POISSON
PERTURBATION 282 VIII CONTENTS PART III APPLICATIONS 285 16 INVARIANT
MEASURES 287 16.1 BASIC DEFINITIONS 287 16.2 EXISTENCE RESULTS 289 16.3
INVARIANT MEASURES FOR THE REACTION-DIFFUSION EQUATION 297 17 LATTICE
SYSTEMS 299 17.1 INTRODUCTION 299 17.2 GLOBAL INTERACTIONS 300 17.3
REGULAR CASE 303 17.4 NON-LIPSCHITZ CASE 305 17.5 KOLMOGOROV'S FORMULA
306 17.6 GIBBS MEASURES 307 18 STOCHASTIC BURGERS EQUATION 312 18.1
BURGERS SYSTEM 312 18.2 UNIQUENESS AND LOCAL EXISTENCE OF SOLUTIONS 314
18.3 STOCHASTIC BURGERS EQUATION WITH ADDITIVE NOISE 317 19
ENVIRONMENTAL POLLUTION MODEL 322 19.1 MODEL 322 20 BOND MARKET MODELS
324 20.1 FORWARD CURVES AND THE HJM POSTULATE * ' ' 324 20.2 HJM
CONDITION 327 20.3 HJMM EQUATION 332 20.4 LINEAR VOLATILITY . ^ 20.5 BGM
EQUATION 347 20.6 CONSISTENCY PROBLEM , 350 APPENDIX A OPERATORS OH
HILBERT SPACES 355 APPENDIX B CO-SEMIGROUPS 365 APPENDIX C
REGULARIZATION OF MARKOV PROCESSES 388 APPENDIX D LTD FORMULAE 391
APPENDIX E LEVY-KHINCHIN FORMULA ON [0 , +OO) 394 APPENDIX F PROOF OF
LEMMA 4.24 396 LIST OF SYMBOLS 399 REFERENCES 403 INDEX 415 |
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| author | Peszat, Szymon 1961- Zabczyk, Jerzy 1941- |
| author_GND | (DE-588)135610680 (DE-588)12135234X |
| author_facet | Peszat, Szymon 1961- Zabczyk, Jerzy 1941- |
| author_role | aut aut |
| author_sort | Peszat, Szymon 1961- |
| author_variant | s p sp j z jz |
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| bvnumber | BV023340249 |
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| callnumber-search | QA274.25 |
| callnumber-sort | QA 3274.25 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 |
| classification_tum | MAT 606f |
| ctrlnum | (OCoLC)228783348 (DE-599)HBZHT015312323 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV023340249 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:01:23Z |
| indexdate | 2024-07-09T21:16:20Z |
| institution | BVB |
| isbn | 9780521879897 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016524027 |
| oclc_num | 228783348 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-824 DE-11 DE-83 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-824 DE-11 DE-83 DE-188 |
| physical | XII, 419 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Peszat, Szymon 1961- Verfasser (DE-588)135610680 aut Stochastic partial differential equations with Lévy noise an evolution equation approach S. Peszat and J. Zabczyk, Institute of Mathematics, Polish Academy of Sciences 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 XII, 419 S. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 113 Literaturverz. S. 403 - 414 Lévy, Processus de Lévy, Processus de ram Équations aux dérivées partielles stochastiques Équations aux dérivées partielles stochastiques ram Lévy-Prozess (DE-588)4463623-4 gnd rswk-swf Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Stochastische partielle Differentialgleichung (DE-588)4135969-0 s Lévy-Prozess (DE-588)4463623-4 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Zabczyk, Jerzy 1941- Verfasser (DE-588)12135234X aut Encyclopedia of mathematics and its applications 113 (DE-604)BV000903719 113 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016524027&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Peszat, Szymon 1961- Zabczyk, Jerzy 1941- Stochastic partial differential equations with Lévy noise an evolution equation approach Encyclopedia of mathematics and its applications Lévy, Processus de Lévy, Processus de ram Équations aux dérivées partielles stochastiques Équations aux dérivées partielles stochastiques ram Lévy-Prozess (DE-588)4463623-4 gnd Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4463623-4 (DE-588)4135969-0 (DE-588)4079013-7 |
| title | Stochastic partial differential equations with Lévy noise an evolution equation approach |
| title_auth | Stochastic partial differential equations with Lévy noise an evolution equation approach |
| title_exact_search | Stochastic partial differential equations with Lévy noise an evolution equation approach |
| title_exact_search_txtP | Stochastic partial differential equations with Lévy noise an evolution equation approach |
| title_full | Stochastic partial differential equations with Lévy noise an evolution equation approach S. Peszat and J. Zabczyk, Institute of Mathematics, Polish Academy of Sciences |
| title_fullStr | Stochastic partial differential equations with Lévy noise an evolution equation approach S. Peszat and J. Zabczyk, Institute of Mathematics, Polish Academy of Sciences |
| title_full_unstemmed | Stochastic partial differential equations with Lévy noise an evolution equation approach S. Peszat and J. Zabczyk, Institute of Mathematics, Polish Academy of Sciences |
| title_short | Stochastic partial differential equations with Lévy noise |
| title_sort | stochastic partial differential equations with levy noise an evolution equation approach |
| title_sub | an evolution equation approach |
| topic | Lévy, Processus de Lévy, Processus de ram Équations aux dérivées partielles stochastiques Équations aux dérivées partielles stochastiques ram Lévy-Prozess (DE-588)4463623-4 gnd Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Lévy, Processus de Équations aux dérivées partielles stochastiques Lévy-Prozess Stochastische partielle Differentialgleichung Wahrscheinlichkeitstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016524027&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000903719 |
| work_keys_str_mv | AT peszatszymon stochasticpartialdifferentialequationswithlevynoiseanevolutionequationapproach AT zabczykjerzy stochasticpartialdifferentialequationswithlevynoiseanevolutionequationapproach |