CONVERGENCE IN PROBABILITY FOR A STOCHASTIC OPTIMAL CONTROL PROBLEMIN THE AVERAGING SCHEMA

Анотація

The article is devoted to the study of the convergence for the problem of stochastic optimal control with Markov switching in the averaging scheme. The combination of the standard Wiener process with a uniformly ergodic Markov process is considered, which enables the description of the system’s evolution under the influence of diffusion noise and random mode switching. Ergodic properties of the fast process and conditions for the regularity of coefficients are provided, ensuring the system’s stable behavior on average. This allows us to prove the convergence in probability (through Lp-estimates) of the trajectories of the original system to the solutions of the marginal averaged system. The obtained results enable the simplification of problem studies in stochastic optimization and optimal control. Keywords: stochastic optimal control, averaging principle, convergence in probability, stochastic differential equations, Wiener process.

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