Yasynskyy V.K., Yurchenko I.V. On the Existence of a Solution to the Cauchy Problem of Nonlinear Stochastic Partial Functional Differential Equations of Special Form // Cybernetics and System Analysis.– 2026.– Vol.62, №2.– P.311-316. - Ясинський, Володимир Кирилович; Юрченко, Ігор Валерійович (Springer Nature Switzerland AG, 2026)
A stochastic model of processes described by systems of nonlinear stochastic partial functional differential equations of a special form is considered, taking into account both diffusive perturbations of the Brownian process type and random perturbations of another type (such as those involving the centered Poisson measure in the equations). The existence of a solution to the Cauchy problem for nonlinear stochastic partial functional differential equations of a special form is proved. The obtained results can be used in the study of the asymptotic stability of solutions of similar systems.
A stochastic model of processes described by systems of nonlinear stochastic partial functional differential equations of a special form is considered, taking into account both diffusive perturbations of the Brownian process type and random perturbations of another type (such as those involving the centered Poisson measure in the equations). The existence of a solution to the Cauchy problem for nonlinear stochastic partial functional differential equations of a special form is proved. The obtained results can be used in the study of the asymptotic stability of solutions of similar systems.
Keywords: nonlinear stochastic partial functional differential equations; random perturbations; Cauchy problem; asymptotic stability of solution