Gorun P. Discrete procedure of stochastic optimization with Markov switchings

The thesis is devoted to the research of behavior and sufficient conditions of discrete stochastic optimization procedure (SOP) in Markov environment under diffusive perturbations in case of balance condition (with equilibrium). It has been established sufficient conditions for the convergence of a discrete SOP to extreme point of averaged system in average and diffusion approximation schemes in the case of diffusive perturbation on the stochastic differencial equation, that also depends on random evolution. Finally, researched procedure was applied to finding optimal investment portfolio for Markovitz model.