UDC 519.21
ON EXISTENCE OF SOLUTION OF THE CAUCHY PROBLEM FOR NONLINEAR
STOCHASTIC PARTIAL DIFFERENTIAL-DIFFERENCE EQUATIONS OF NEUTRAL TYPE
Abstract. The authors consider the existence of the solution of 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.
Keywords: stochastic partial differential equations of neutral type, existence of the solution with probability one, Cauchy problem.
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