Solutions of SPDE’s Associated with a Stochastic Flow

Article Type

Research Article

Publication Title

Potential Analysis

Abstract

We consider the following stochastic partial differential equation,dYt=L∗Ytdt+A∗Yt⋅dBtY0=ψ,associated with a stochastic flow {X(t,x)}, for t ≥ 0, x∈ ℝd, as in Rajeev and Thangavelu (Potential Anal. 28(2), 139–162, 2008). We show that the strong solutions constructed there are ‘locally of compact support’. Using this notion,we define the mild solutions of the above equation and show the equivalence between strong and mild solutions in the multi Hilbertian space S′. We show uniqueness of solutions in the case when ψ is smooth via the ‘monotonicity inequality’ for (L∗,A∗), which is a known criterion for uniqueness.

First Page

203

Last Page

221

DOI

10.1007/s11118-019-09764-0

Publication Date

6-1-2020

Comments

Open Access, Green

This document is currently not available here.

Share

COinS