Some Properties of Solutions of Double Stochastic Differential Equations

The paper deals with double stochastic differential equations. Existence and uniqueness are obtained under a Holder-type hypothesis. The convergence in probability of the successive approximations in the Holder norm and the existence of a weak solution for continuous coefficients are also proved. Under an additional independence hypothesis, the mean square convergence of fractional step approximations is shown. This last result is used in order to deduce a comparison result and as a consequence the existence of a strong solution in the case when the “double “noise is additive.