We prove a uniqueness result for the stochastic transport linear equation (STLE), without any W(1.1) or BV hypothesis on the coefficient, which is needed for the corresponding deterministic equation. We use Wiener chaos decomposition to pass from the STLE to a deterministic second-order transport equation with uniqueness property.
Wiener chaos and uniqueness for stochastic transport equation = Chaos de Wiener et unicité pour l’équation de transport stochastique / M. Maurelli. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - 349:11-12(2011), pp. 669-672.
Wiener chaos and uniqueness for stochastic transport equation = Chaos de Wiener et unicité pour l’équation de transport stochastique
M. Maurelli
2011
Abstract
We prove a uniqueness result for the stochastic transport linear equation (STLE), without any W(1.1) or BV hypothesis on the coefficient, which is needed for the corresponding deterministic equation. We use Wiener chaos decomposition to pass from the STLE to a deterministic second-order transport equation with uniqueness property.
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