Format:
1 Online-Ressource (xii, 419 pages)
,
digital, PDF file(s)
ISBN:
9780511721373
Series Statement:
Encyclopedia of mathematics and its applications volume 113
Content:
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
Content:
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
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9780521879897
Additional Edition:
Erscheint auch als Druckausgabe Peszat, Szymon, 1961 - Stochastic partial differential equations with Lévy Noise New York : Cambridge University Press, 2007 ISBN 9780521879897
Language:
English
Subjects:
Mathematics
Keywords:
Stochastische partielle Differentialgleichung
;
Lévy-Prozess
;
Wahrscheinlichkeitstheorie
DOI:
10.1017/CBO9780511721373
Author information:
Zabczyk, Jerzy 1941-
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