$L^{p}-$solutions of the stochastic transport equation
Functional Analysis
2011-03-22 v2 Probability
Abstract
We consider the stochastic transport linear equation and we prove existence and uniqueness of weak solutions. Moreover, we obtain a representation of the general solution and a Wong-Zakai principle for this equation. We make only minimal assumptions, similar to the deterministic problem. The proof is supported on the generalized It\^o-Ventzel-Kunita formula (see 15) and the theory of Lions-DiPerna on transport linear equation (see 9).
Keywords
Cite
@article{arxiv.1102.3076,
title = {$L^{p}-$solutions of the stochastic transport equation},
author = {Pedro Catuogno and Christian Olivera},
journal= {arXiv preprint arXiv:1102.3076},
year = {2011}
}
Comments
Changed Intrododuction, bibliography