Abstract. For Markov statistical experiments in a balanced random environment, defined by solutions of difference stochastic equations, an approximation is obtained in series scheme, by the Ornstein–Uhlenbeck diffusion process. The drift and diffusion parameters are determined by averaging over the stationary distribution of the embedded Markov chain using the balance condition.

Keywords: statistical experiment, stochastic difference equations, Markov random environment, guiding parameter of the regression function of increments, diffusion coefficient of a stochastic component, Ornstein–Uhlenbeck type diffusion process.