Differential diffusion model with two equilibrium states

Abstract

The difference diffusion model with two equilibrium states is given by a stochastic equation with two components: the predicted one, which is determined by the regression function of increments with two equilibriums, and the stochastic one, which is the martingale difference. We propose a classification of zones of influence of equilibriums according to asymptotic properties of trajectories of statistical experiments. We study asymptotic behavior of statistical experiments, determined by the sums of $N$ sample values, as $N\to\infty$.