The Annals of Probability

Wiener chaos solutions of linear stochastic evolution equations

S. V. Lototsky and B. L. Rozovskii

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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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Ann. Probab., Volume 34, Number 2 (2006), 638-662.

First available in Project Euclid: 9 May 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 60H40: White noise theory

Feynmann–Kac formula generalized random elements stochastic parabolic equations turbulent transport white noise


Lototsky, S. V.; Rozovskii, B. L. Wiener chaos solutions of linear stochastic evolution equations. Ann. Probab. 34 (2006), no. 2, 638--662. doi:10.1214/009117905000000738.

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