Multidimensional linear stochastic differential equations in the skorohod sense

Abstract

We study multidimensional linear Skorohod stochastic differential equations driven by a one-dimensional Wiener process, assuming that the initial condition and the diffusion and drift coefficients are functions of a finite-dimensional Gaussian vector belonging to the first Wiener chaos. We transform this equation into an adapted stochastic hyperbolic partial differential equation, and we establish the existence and uniqueness of the solution for such an equation by means of suitable energy inequalities in two particular cases: i) when the diffusion matrix σt has the form ii) when the coefficients possess holomorphic extensions in a neighborhood of the real axis