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
Full-text PDF Free Access
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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
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.