Differential diffusion model with two equilibrium states

TL;DR

This paper introduces a stochastic differential model with two equilibrium states, analyzing its asymptotic behavior and classifying influence zones based on the trajectories of statistical experiments.

Contribution

It proposes a new differential diffusion model with dual equilibria and classifies influence zones using asymptotic properties of trajectories.

Findings

Asymptotic behavior of the model is characterized as sample size grows large.

Classification of zones of influence based on equilibrium states.

Analysis of the model's statistical experiment trajectories.

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 $N\to\infty$.