On existence of solutions to stochastic differential equations with osmotic velocities

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 processes constructed in terms of those derivatives. The paper is devoted to investigation of stochastic differential equations with osmotic velocities, i.e., with Nelson's antisymmetric mean derivatives. Since the osmotic velocities of stochastic processes shows "how fast the randomness grows", such research is important for investigation of models of physical processes that take into account stochastic properties. An existence of solution theorem for those equations is obtained.