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SPDEs with α-Stable Lévy Noise : A Random Field Approach
Author
Source
International Journal of Stochastic Analysis
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-02-04
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
This paper is dedicated to the study of a nonlinear SPDE on a bounded domain in Rd, with zero initial conditions and Dirichlet boundary, driven by an α-stable Lévy noise Z with α∈(0,2), α≠1, and possibly nonsymmetric tails.
To give a meaning to the concept of solution, we develop a theory of stochastic integration with respect to this noise.
The idea is to first solve the equation with “truncated” noise (obtained by removing from Z the jumps which exceed a fixed value K), yielding a solution uK, and then show that the solutions uL,L>K coincide on the event t≤τK, for some stopping times τK converging to infinity.
A similar idea was used in the setting of Hilbert-space valued processes.
A major step is to show that the stochastic integral with respect to ZK satisfies a pth moment inequality.
This inequality plays the same role as the Burkholder-Davis-Gundy inequality in the theory of integration with respect to continuous martingales.
American Psychological Association (APA)
Balan, Raluca M.. 2014. SPDEs with α-Stable Lévy Noise : A Random Field Approach. International Journal of Stochastic Analysis،Vol. 2014, no. 2014, pp.1-22.
https://search.emarefa.net/detail/BIM-498564
Modern Language Association (MLA)
Balan, Raluca M.. SPDEs with α-Stable Lévy Noise : A Random Field Approach. International Journal of Stochastic Analysis No. 2014 (2014), pp.1-22.
https://search.emarefa.net/detail/BIM-498564
American Medical Association (AMA)
Balan, Raluca M.. SPDEs with α-Stable Lévy Noise : A Random Field Approach. International Journal of Stochastic Analysis. 2014. Vol. 2014, no. 2014, pp.1-22.
https://search.emarefa.net/detail/BIM-498564
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-498564