On global in time existence of solutions to stochastic equations with backward mean derivatives

The notion of mean derivatives was introduced by E. Nelson in 60-th years of XX century and at the moment there are a lot of mathematical models of physical and technical processes constructed in terms of equations with those derivatives. The paper is devoted to investigation of stochastic differential equations with backward mean derivatives. This type of equations arise in several models of physical and technical processes and so its investigation is important for applications. But on the other hand, the investigation of such equations requires new methods and ideas. In this paper we deal with the property of global in time existence of all solutions of "inverse" Cauchy problem for equations with backward mean derivatives. A condition that guarantees the global in time existence of such solutions is obtained. This result is useful for many mathematical models of physical and technical processes.