Regularity of Solutions to Bilinear Stochastic Wave Equations

The paper is concerned with strong solutions of bilinear stochastic wave equations in ℛ d , of which the coefficients contain semimartingale white noises with spatial parameters. For the Cauchy problems, the existence and spatial regularity of solutions in Sobolev spaces are proved under appropriate...

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Bibliographic Details
Published in:Stochastic analysis and applications 2004-11, Vol.22 (6), p.1609-1631
Main Author: Chow, Pao-Liu
Format: Article
Language:English
Subjects:
35R
60G
62G
Energy inequalities
Exact sciences and technology
Mathematical analysis
Mathematics
Nonparametric inference
Partial differential equations
Probability and statistics
Probability theory and stochastic processes
Regularity of solution
Sciences and techniques of general use
Statistics
Stochastic processes
Stochastic wave equation
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Summary:The paper is concerned with strong solutions of bilinear stochastic wave equations in ℛ d , of which the coefficients contain semimartingale white noises with spatial parameters. For the Cauchy problems, the existence and spatial regularity of solutions in Sobolev spaces are proved under appropriate conditions. The dependence of solution regularity on the smoothness of the random coefficients is ascertained. The proofs are based on stochastic energy inequalities, the semigroup method and certain submartingale inequalities. Regularity results are also obtained for the special case of Wiener semimartingales.
ISSN:0736-2994
1532-9356
DOI:10.1081/SAP-200029500