LINEAR SKOROHOD STOCHASTIC DIFFERENTIAL-EQUATIONS

Let sigma and b be bounded processes on the Wiener space (OMEGA, F, P), OMEGA = C([0, 1]), which are possibly anticipating the Brownian motion W(t)(omega) = omega(t), and let eta be a bounded random variable. We deduce the existence and uniqueness of a solution X for the linear equation with Skorohod integral X(t) = eta + integral 0t sigma-sX(s)dW(s) + integral 0t b(s)X(s)ds, t is-an-element-of [0, 1], under rather weak assumptions on sigma and no additional requirement on b and eta. The description of the solution X requires to study the family {T(t), t is-an-element-of [0, 1]} of transformations T(t) of OMEGA into itself associated to (1) by the equation T(t) = omega + integral 0t sigma-s(T(s)omega)ds, omega is-an-element-of OMEGA, t is-an-element-of [0, 1].