Solving SPDEs driven by colored noise: A chaos approach

Lototsky, S.; Stemmann, K.

doi:10.1090/S0033-569X-08-01088-2

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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