Asymptotic behavior of solutions of some classes of stochastic equations and their applications to statistical problems

Abstract

Conditions of stability and asymptotic normality are derived for solutions of equations of form\(\sum _{k = 1}^n f(\theta , \eta _k , x_k ) = \sum _{k = 1}^n \xi _k\). Heref(θ, ·) is a family of functions and (ξk, ηk) is a sequence of conditionally independent variables inRr given on xk, k≥1, where xk is a sequence with values in an arbitrary space that satisfies a certain ergodicity condition. The continuous-time case is also considered. The asymptotic properties of maximum likelihood estimators and moment method estimators are investigated for observation of weakly dependent variables.