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Existence of the Solution to the Cauchy Problem for Nonlinear Stochastic Partial Differential-Difference Equations of Neutral Type

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.

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Correspondence to V. K. Yasynskyy.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 5, September–October, 2021, pp. 108–119.

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Yasynskyy, V.K., Yurchenko, I.V. Existence of the Solution to the Cauchy Problem for Nonlinear Stochastic Partial Differential-Difference Equations of Neutral Type. Cybern Syst Anal 57, 764–774 (2021). https://doi.org/10.1007/s10559-021-00401-6

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  • DOI: https://doi.org/10.1007/s10559-021-00401-6

Keywords

  • stochastic partial differential equations of neutral type
  • existence of the solution with probability one
  • Cauchy problem