Hyperbolic stochastic differential equations: Absolute continuity of the law of the solution at a fixed point

Let W be the Wiener process on T = [0, 1]2. Consider the stochastic integral equation (Equation Presented) where Rζ = {(s′, t′) ∈ T: s′ ≤ s, t′ ≤ t}, ζ = (s, t) ∈ T, and x0 ∈ ℝ. Under some assumptions on the coefficients ai, the existence and uniqueness of a solution for this stochastic integral equation is already known (see [6]). In this paper we present some sufficient conditions for the law of Xζ to have a density. © 1996 Springer-Verlag New York Inc.