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<p>A stochastic model is considered for processes described by systems of nonlinear stochastic partial functional differential equations of a special form, accounting for both Brownian-type diffusion perturbations 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 of similar systems.</p>

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On the Existence of a Solution to the Cauchy Problem of Nonlinear Stochastic Partial Functional Differential Equations of Special Form

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • I. V. Yurchenko,
  • V. K. Yasynskyy

摘要

A stochastic model is considered for processes described by systems of nonlinear stochastic partial functional differential equations of a special form, accounting for both Brownian-type diffusion perturbations 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 of similar systems.