Statistical experiments with persistent linear regression in the Markov random medium

Abstract

The statistical experiments (SE) with persistent non-linear regression are considered in the discrete-continuous time k=[Nt]k=[Nt], 0≤t≤T0≤t≤T. The directing parameters of the regression function increments depend on the state of an embedded Markov chain in the (homogeneous in time) uniformly ergodic Markov process, which describes the states of the random medium. SE are defined by the solutions of stochastic difference equations with two components: predictive and stochastic (martingale-difference). The obtained approximation in the series scheme with series parameter NN (size of the sample), as N→∞N→∞, is a diffusion Ornstein–Uhlenbeck-type process. The parameters of drift and diffusion are determined by averaging over the stationary distribution of the embedded Markov chain.