Polshkov Y. Optimal estimation and control in systems with fast random oscillations

Differential equations with "physical" white noise. Investigate convergence rate of differential equations solutions with fast random oscillations to Ito equations solutions. Construct sufficient controls in systems; obtain the quasi-maximal likelihood estimators of the unknown parameter; investigate the properties of the estimate of the least squares method for the unknown parameter; generalize the optimum consumption-portfolio Merton model in security market; construct optimum portfolio; obtain the estimates of discounted utility.