Stochastic partial differential equations with Lévy noise: an evolution equation approach
Recent years have seen an explosion of interest in stochastic partial differential equations where the driving noise is discontinuous. In this comprehensive monograph, two leading experts detail the evolution equation approach to their solution. Most of the results appeared here for the first time i...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2007
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| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 113 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 TUM01 Volltext |
| Zusammenfassung: | Recent years have seen an explosion of interest in stochastic partial differential equations where the driving noise is discontinuous. In this comprehensive monograph, two leading experts detail the evolution equation approach to their solution. Most of the results appeared here for the first time in book form. The authors start with a detailed analysis of Lévy processes in infinite dimensions and their reproducing kernel Hilbert spaces; cylindrical Lévy processes are constructed in terms of Poisson random measures; stochastic integrals are introduced. Stochastic parabolic and hyperbolic equations on domains of arbitrary dimensions are studied, and applications to statistical and fluid mechanics and to finance are also investigated. Ideal for researchers and graduate students in stochastic processes and partial differential equations, this self-contained text will also interest those working on stochastic modeling in finance, statistical physics and environmental science |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xii, 419 pages) |
| ISBN: | 9780511721373 |
| DOI: | 10.1017/CBO9780511721373 |
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| 505 | 8 | |a 1. Why equations with Levy noise? -- 2. Analytic preliminaries -- 3. Probabilistic preliminaries -- 4. Levy processes -- 5. Levy semigroups -- 6. Poisson random measures -- 7. Cylindrical processes and reproducing kernels -- 8. Stochastic integration -- 9. General existence and uniqueness results -- 10. Equations with non-Lipschitz coefficients -- 11. Factorization and regularity -- 12. Stochastic parabolic problems -- 13. Wave and delay equations -- 14. Equations driven by a spatially homogeneous noise -- 15. Equations with noise on the boundary -- 16. Invariant measures -- 17. Lattice systems -- 18. Stochastic Burgers equation -- 19. Environmental pollution model -- 20. Bond market models -- App. A. Operators on Hilbert spaces -- App. B. Co-semigroups -- App. C. Regularization of Markov processes -- App. D. Ito formulae -- App. E. Levy-Khinchin formula on [0, + [infinity]) -- App. F. Proof of Lemma 4.24 | |
| 520 | |a Recent years have seen an explosion of interest in stochastic partial differential equations where the driving noise is discontinuous. In this comprehensive monograph, two leading experts detail the evolution equation approach to their solution. Most of the results appeared here for the first time in book form. The authors start with a detailed analysis of Lévy processes in infinite dimensions and their reproducing kernel Hilbert spaces; cylindrical Lévy processes are constructed in terms of Poisson random measures; stochastic integrals are introduced. Stochastic parabolic and hyperbolic equations on domains of arbitrary dimensions are studied, and applications to statistical and fluid mechanics and to finance are also investigated. Ideal for researchers and graduate students in stochastic processes and partial differential equations, this self-contained text will also interest those working on stochastic modeling in finance, statistical physics and environmental science | ||
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Datensatz im Suchindex
| _version_ | 1804176884361068544 |
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| any_adam_object | |
| author | Peszat, Szymon 1961- |
| author_GND | (DE-588)135610680 (DE-588)12135234X |
| author_facet | Peszat, Szymon 1961- |
| author_role | aut |
| author_sort | Peszat, Szymon 1961- |
| author_variant | s p sp |
| building | Verbundindex |
| bvnumber | BV043942003 |
| classification_rvk | SK 820 |
| classification_tum | MAT 606f |
| collection | ZDB-20-CBO |
| contents | 1. Why equations with Levy noise? -- 2. Analytic preliminaries -- 3. Probabilistic preliminaries -- 4. Levy processes -- 5. Levy semigroups -- 6. Poisson random measures -- 7. Cylindrical processes and reproducing kernels -- 8. Stochastic integration -- 9. General existence and uniqueness results -- 10. Equations with non-Lipschitz coefficients -- 11. Factorization and regularity -- 12. Stochastic parabolic problems -- 13. Wave and delay equations -- 14. Equations driven by a spatially homogeneous noise -- 15. Equations with noise on the boundary -- 16. Invariant measures -- 17. Lattice systems -- 18. Stochastic Burgers equation -- 19. Environmental pollution model -- 20. Bond market models -- App. A. Operators on Hilbert spaces -- App. B. Co-semigroups -- App. C. Regularization of Markov processes -- App. D. Ito formulae -- App. E. Levy-Khinchin formula on [0, + [infinity]) -- App. F. Proof of Lemma 4.24 |
| ctrlnum | (ZDB-20-CBO)CR9780511721373 (OCoLC)850537950 (DE-599)BVBBV043942003 |
| 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 |
| doi_str_mv | 10.1017/CBO9780511721373 |
| format | Electronic eBook |
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| id | DE-604.BV043942003 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511721373 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350973 |
| oclc_num | 850537950 |
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| publishDate | 2007 |
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| publisher | Cambridge University Press |
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| 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 Cambridge Cambridge University Press 2007 1 online resource (xii, 419 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 113 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 1. Why equations with Levy noise? -- 2. Analytic preliminaries -- 3. Probabilistic preliminaries -- 4. Levy processes -- 5. Levy semigroups -- 6. Poisson random measures -- 7. Cylindrical processes and reproducing kernels -- 8. Stochastic integration -- 9. General existence and uniqueness results -- 10. Equations with non-Lipschitz coefficients -- 11. Factorization and regularity -- 12. Stochastic parabolic problems -- 13. Wave and delay equations -- 14. Equations driven by a spatially homogeneous noise -- 15. Equations with noise on the boundary -- 16. Invariant measures -- 17. Lattice systems -- 18. Stochastic Burgers equation -- 19. Environmental pollution model -- 20. Bond market models -- App. A. Operators on Hilbert spaces -- App. B. Co-semigroups -- App. C. Regularization of Markov processes -- App. D. Ito formulae -- App. E. Levy-Khinchin formula on [0, + [infinity]) -- App. F. Proof of Lemma 4.24 Recent years have seen an explosion of interest in stochastic partial differential equations where the driving noise is discontinuous. In this comprehensive monograph, two leading experts detail the evolution equation approach to their solution. Most of the results appeared here for the first time in book form. The authors start with a detailed analysis of Lévy processes in infinite dimensions and their reproducing kernel Hilbert spaces; cylindrical Lévy processes are constructed in terms of Poisson random measures; stochastic integrals are introduced. Stochastic parabolic and hyperbolic equations on domains of arbitrary dimensions are studied, and applications to statistical and fluid mechanics and to finance are also investigated. Ideal for researchers and graduate students in stochastic processes and partial differential equations, this self-contained text will also interest those working on stochastic modeling in finance, statistical physics and environmental science Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Lévy-Prozess (DE-588)4463623-4 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- Sonstige (DE-588)12135234X oth Erscheint auch als Druckausgabe 978-0-521-87989-7 Encyclopedia of mathematics and its applications volume 113 (DE-604)BV000903719 volume 113 https://doi.org/10.1017/CBO9780511721373 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Peszat, Szymon 1961- Stochastic partial differential equations with Lévy noise an evolution equation approach Encyclopedia of mathematics and its applications 1. Why equations with Levy noise? -- 2. Analytic preliminaries -- 3. Probabilistic preliminaries -- 4. Levy processes -- 5. Levy semigroups -- 6. Poisson random measures -- 7. Cylindrical processes and reproducing kernels -- 8. Stochastic integration -- 9. General existence and uniqueness results -- 10. Equations with non-Lipschitz coefficients -- 11. Factorization and regularity -- 12. Stochastic parabolic problems -- 13. Wave and delay equations -- 14. Equations driven by a spatially homogeneous noise -- 15. Equations with noise on the boundary -- 16. Invariant measures -- 17. Lattice systems -- 18. Stochastic Burgers equation -- 19. Environmental pollution model -- 20. Bond market models -- App. A. Operators on Hilbert spaces -- App. B. Co-semigroups -- App. C. Regularization of Markov processes -- App. D. Ito formulae -- App. E. Levy-Khinchin formula on [0, + [infinity]) -- App. F. Proof of Lemma 4.24 Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Lévy-Prozess (DE-588)4463623-4 gnd |
| subject_GND | (DE-588)4135969-0 (DE-588)4079013-7 (DE-588)4463623-4 |
| 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_full | Stochastic partial differential equations with Lévy noise an evolution equation approach S. Peszat and J. Zabczyk |
| title_fullStr | Stochastic partial differential equations with Lévy noise an evolution equation approach S. Peszat and J. Zabczyk |
| title_full_unstemmed | Stochastic partial differential equations with Lévy noise an evolution equation approach S. Peszat and J. Zabczyk |
| 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 | Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Lévy-Prozess (DE-588)4463623-4 gnd |
| topic_facet | Stochastische partielle Differentialgleichung Wahrscheinlichkeitstheorie Lévy-Prozess |
| url | https://doi.org/10.1017/CBO9780511721373 |
| volume_link | (DE-604)BV000903719 |
| work_keys_str_mv | AT peszatszymon stochasticpartialdifferentialequationswithlevynoiseanevolutionequationapproach AT zabczykjerzy stochasticpartialdifferentialequationswithlevynoiseanevolutionequationapproach |