Gololobov D. Method of empirical average in the problems of parameter estimation and optimization for multidimensional stochastic systems

The empirical estimates of the unknown parameter of homogenous in a narrow sense multidimensional stochastic systems with continuous time observed in a cube (under conditions of ergodicity), parallelepiped and circle (under conditions of strong mixing) were considered. Non-stationary multidimensional stochastic models with discrete and continuous time and strong mixing were examined. It was investigated the asymptotic behavior (strong consistency and asymptotic distribution) of the estimates mentioned above. It was obtained the asymptotic distribution for models of multidimensional stochastic systems with continuous time and strong mixing observed in a parallelepiped and circle under restrictions on the parameter in the form of inequalities. The asymptotic distribution for non-stationary models with discrete and continuous time and strong mixing under restrictions on the parameter in the form of inequalities was constructed.