Statistical experiments in a balanced Markov random environment (Q904430)

Markov statistical experiments with discrete-continuous time are defined by solutions of stochastic difference equations with the drift and diffusion parameters dependent on states of the balanced Markov random environment providing the zero mean of the guiding regression function of increments by the ergodic distribution of the embedded Markov chain. Markov statistical experiments defined by solutions of stochastic difference equations under additional conditions admit the approximation in a scheme of series with the series parameter tending to zero and a normal Ornstein-Uhlenbeck-type process in continuous time. In this case, an algorithm for computing the parameter of the guiding action and dispersion of the stochastic component of the limit process changes essentially. The main results are given in Theorem 1 and the results of the perturbation and stationary of the limit process are given in Lemmas 1, 2 and 3.