Stochastic partial differential equations with Lévy noise : an evolution equation approach / S. Peszat and J. Zabczyk.
Material type:
TextSeries: Encyclopedia of mathematics and its applications ; volume 113.Publisher: Cambridge : Cambridge University Press, 2007Description: 1 online resource (xii, 419 pages)Content type: - text
- computer
- online resource
- 9781107089754
- 1107089751
- 9781107096059
- 1107096057
- 1139883437
- 9781139883436
- 1107101654
- 9781107101654
- 1107104084
- 9781107104082
- 0511721374
- 9780511721373
- Stochastic partial differential equations
- Lévy processes
- Équations aux dérivées partielles stochastiques
- Lévy, Processus de
- MATHEMATICS -- Calculus
- MATHEMATICS -- Mathematical Analysis
- Lévy processes
- Stochastic partial differential equations
- Stochastische differentiaalvergelijkingen
- Partiële differentiaalvergelijkingen
- 515.353 22
- QA274.25 .P47 2007eb
- 31.70
- 31.45
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Includes bibliographical references (pages 403-414) and index.
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.
Print version record.
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.
English.
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