Khimka U. Stochastic Optimization Procedure in Sheme Series with Markov Perturbations

The thesis for obtaining the Candidate of Physical and Mathematical Sciences degree on the speciality 01.05.04 – Systemny Analysis and theory of making desicion. – Taras Shevchenko National University of Kiev of Ministry of Education and Science of Ukraine, Kiev, 2013. In the thesis, author obtain sufficient conditions for the convergence of stochastic optimization procedure with depend Markov process of regression function in the average scheme and the diffusion approximation scheme. It is investigated the asymptotic normality of the stochastic optimization procedure. It is prove conditions for the convergence of fluctuations stochastic optimization procedure with impulse and diffusion perturbing. Appropriate limit processes view are discovered. Asymptotic representation of the perturbed generator procedure was built for this purpose. It is proposed to used continuous stochastic optimization procedure in software reability.