Про існування розв’язку задачі Коші для нелінійного дифузійного стохастичного диференціально-різницевого рівняння нейтрального типу в частинних похідних з урахуванням випадкових зовнішних збурень - Yasynskyy, V. K.; Yurchenko, I. V. (The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", 2017)
The question related to the existence of the Cauchy problem solution in the class of nonlinear diffusion stochastic partial differential-difference equations of a neutral type with random external disturbances which are independent from the Wiener process is considered. Sufficient conditions are obtained for the diffusion coefficients of nonlinear stochastic differential-difference equations of a neutral type (NDSDRRNT) that guarantee the existence of the solution with the probability of 1. The method of the proof is based on the results of O.M. Stanzhitsky and A.O. Tsukanova on the existence and uniqueness of the Cauchy problem solution for the stochastic differential reaction-diffusion equation of a neutral type. In this paper, we prove the existence of a "mild solution" of NDSDRRNT. In some cases, such equations are mathematical models of real processes, the consideration of which is planned in the future work.