Kukurba V. Continues Stochastic Optimization Procedure with semi-Markov switchings

In the thesis, author obtain sufficient conditions for the convergence of stochastic optimization procedure that depends on semi-Markov process of regression function in the average scheme and the diffusion approximation scheme. Asymptotic normality of the stochastic optimization procedure is investigated in the diffusion approximation scheme. Extended compensating operators, constructed on Markov renewal process, are used for characterization of semi-Markov continuous random evolution in schemes. Conditions are obtained for the convergence of fluctuations stochastic optimization procedure with diffusion perturbing. Appropriate limit processes view are discovered. Asymptotic representation of the perturbed generator procedure was built for this purpose. The continuous process stochastic optimization with an additional impulse perturbing is considered. Obtained sufficient conditions for convergence allows to consider the asymptotic normality of the procedure.