Covariation analysis of the linean Markov iterations

Abstract

The paper analyzes the behavior of the first and second moments of linear difference equations with Markov coefficients. A convenient for application method of asymptotic stability analysis for equations with close to constant coefficients is proposed. By applying the Kato perturbation theory, we have developed an algorithm based on the decomposition by the small parameter powers of the specially constructed operator. In the case of independent perturbations, the method proposed makes it possible to write necessary and sufficient conditions for stability in the quadratic mean in the form of inequalities with coefficients.