Yasynskyy, V.K., Yurchenko, I.V. Existence of the Solution to the Cauchy Problem for Nonlinear Stochastic Partial Differential-Difference Equations of Neutral Type // Cybernetics and Systems Analysis.– 2021.– Vol.57.– No.5.– P.764–774.

Abstract

The authors consider the existence of the solution to the Cauchy problem in the class of nonlinear stochastic partial differential-difference equations of neutral type, with regard for random external perturbations independent of the Wiener process. Sufficient conditions are obtained for the coefficients of the nonlinear stochastic differential-difference equations of neutral type that guarantee the existence of the solution with probability one.