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March 2006 Wiener chaos solutions of linear stochastic evolution equations
S. V. Lototsky, B. L. Rozovskii
Ann. Probab. 34(2): 638-662 (March 2006). DOI: 10.1214/009117905000000738


A new method is described for constructing a generalized solution of a stochastic evolution equation. Existence, uniqueness, regularity and a probabilistic representation of this Wiener Chaos solution are established for a large class of equations. As an application of the general theory, new results are obtained for several types of the passive scalar equation.


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S. V. Lototsky. B. L. Rozovskii. "Wiener chaos solutions of linear stochastic evolution equations." Ann. Probab. 34 (2) 638 - 662, March 2006.


Published: March 2006
First available in Project Euclid: 9 May 2006

zbMATH: 1100.60034
MathSciNet: MR2223954
Digital Object Identifier: 10.1214/009117905000000738

Primary: 60H15
Secondary: 35R60 , 60H40

Keywords: Feynmann–Kac formula , generalized random elements , Stochastic parabolic equations , turbulent transport , White noise

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 2 • March 2006
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