Yurchenko I.V. The existence of the solution of the Cauсhi problem for nonlinear stochastic partial differential-difference equations of neutral type with random external perturbances // Scientific World Journal.– 2022.– Issue №13, Part 1.– P.54–64.– Published by Academy of Economics named after D.A. Tsenov, Bulgaria (jointly with SWorld).

Abstract

The question of the existence of a solution of the Cauchy problem in the class of nonlinear stochastic differential-difference equations of neutral type in partial derivatives with respect to random external perturbations independent of the Wiener process is considered. Sufficient conditions are obtained for the coefficients of the nonlinear stochastic differential-difference equation of the neutral type, which guarantee the existence with probability of the unit of its solution.