On the first quasiderivatives of solutions of Ito stochastic equations

In the study of smoothness of probabilistic solutions of differential equations an important role is played by the derivatives of the solutions of stochastic equations with respect to the initial data. In this article the possibility of replacing them by other processes called quasiderivatives is considered. As examples of the advantage of such a substitution, the intrinsic smoothness of probabilistic solutions in a domain is proved in several cases.