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- Title
L<sup>p</sup>-solutions of the stochastic transport equation.
- Authors
Catuogno, Pedro; Olivera, Christian
- Abstract
We consider the stochastic transport linear equation and we prove existence and uniqueness of weak Lp-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 Itô-Ventzel-Kunita formula and the theory of Lions-DiPerna on transport linear equation.
- Subjects
STOCHASTIC differential equations; TRANSPORT theory; LINEAR equations; MATHEMATICAL proofs; EXISTENCE theorems; REPRESENTATIONS of algebras
- Publication
Random Operators & Stochastic Equations, 2013, Vol 21, Issue 2, p125
- ISSN
0926-6364
- Publication type
Article
- DOI
10.1515/rose-2013-0007