STOCHASTIC EVOLUTION UNDER MARKOV-MODULATED POISSON PERTURBATION IN THE DIFFUSION APPROXIMATION SCHEME

The authors study the asymptotic behavior of stochastic evolutionary systems with Markov-modulated Poisson perturbation in the diffusion approximation scheme. They consider combining the Poisson process with the Markov process, which allows for describing random transitions between different modes of evolution. The ergodic properties of the Markov-modulated Poisson process that ensure the stable behavior of the system on average are presented. Boundary generators for the original system of stochastic differential equations are constructed. The results allow for studying stochastic optimization and optimal control problems. Keywords: stochastic evolution, Markov-modulated Poisson process, diffusion approximation schema.