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<p>The authors studied the asymptotic behavior of stochastic evolutionary systems with Markov-modulated Poisson perturbation in the diffusion approximation scheme. They considered combining the Poisson process with the Markov process, which enables describing random transitions between different modes of evolution. The authors presented the ergodic properties of the Markov-modulated Poisson process that ensure the stable system’s behavior on average. They also constructed limit generators for the original system of stochastic differential equations. The results allow for studying stochastic optimization and optimal control problems.</p>

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Stochastic Evolution Under Markov-Modulated Poisson Perturbation in the Diffusion Approximation Scheme

  • 期刊论文

  • 发表日期：

    2025年5月30日

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  • Ya. M. Chabanyuk,
  • S. A. Semenyuk,
  • U. T. Khimka,
  • R. A. Chypurko

摘要

The authors studied the asymptotic behavior of stochastic evolutionary systems with Markov-modulated Poisson perturbation in the diffusion approximation scheme. They considered combining the Poisson process with the Markov process, which enables describing random transitions between different modes of evolution. The authors presented the ergodic properties of the Markov-modulated Poisson process that ensure the stable system’s behavior on average. They also constructed limit generators for the original system of stochastic differential equations. The results allow for studying stochastic optimization and optimal control problems.