Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Solving SPDEs driven by colored noise: A chaos approach

Authors: S. V. Lototsky and K. Stemmann
Journal: Quart. Appl. Math. 66 (2008), 499-520
MSC (2000): Primary 60H15; Secondary 35R60, 60H40
DOI: https://doi.org/10.1090/S0033-569X-08-01088-2
Published electronically: July 2, 2008
MathSciNet review: 2445526
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Abstract: An Itô-Skorokhod bilinear equation driven by infinitely many independent colored noises is considered in a normal triple of Hilbert spaces. The special feature of the equation is the appearance of the Wick product in the definition of the Itô-Skorokhod integral, requiring innovative approaches to computing the solution. A chaos expansion of the solution is derived and several truncations of this expansion are studied. A recursive approximation of the solution is suggested and the corresponding approximation error bound is computed.

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Additional Information

S. V. Lototsky
Affiliation: Department of Mathematics, USC, Los Angeles, California 90089
Email: lototsky@math.usc.edu

K. Stemmann
Affiliation: Department of Mathematics, USC, Los Angeles, California 90089

DOI: https://doi.org/10.1090/S0033-569X-08-01088-2
Keywords: Generalized random fields, Malliavin calculus, Skorokhod integral, Wiener chaos
Received by editor(s): May 15, 2007
Published electronically: July 2, 2008
Additional Notes: The first author acknowledges support from the NSF CAREER award DMS-0237724.
The work of K. Stemmann was partially supported by the NSF Grant DMS-0237724
Article copyright: © Copyright 2008 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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