Linear stochastic differential equations and Wick products (Q1333582)

We establish the existence and uniqueness of the solution to a multidimensional linear Skorokhod stochastic differential equation with deterministic diffusion matrix, using the notions of Wick product and \(S\)-transform. If the diffusion matrix is constant and has real eigenvalues, the solution is a stochastic process with moments of all orders, provided that the initial condition is differentiable up to a suitable order. The case of a diffusion matrix in the first Wiener chaos is discussed in the last section.