ON THE EXISTENCE OF A SOLUTION TO THE CAUCHY PROBLEM FOR NONLINEAR STOCHASTIC PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS OF A SPECIAL FORM
Анотація
A stochastic model of processes described by systems of nonlinear stochastic partial differential functional equations of special form is considered, taking into account both diffusion disturbances of the Brownian process type and Poisson switching. The existence of a solution to the Cauchy problem for such systems is proved. The results obtained can be used to study the asymptotic stability of solutions to similar systems. Keywords: stochastic partial functional differential equations, existence of a solution.
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