Abstract. A difference diffusion model with two equilibrium states is given by a stochastic equation with two components: a predictable one, defined by increments regression function with two equilibrium states and a stochastic one, which is a martingale difference. Zone classification based on the asymptotic properties of the trajectories of statistical experiments is proposed. The asymptotic behavior of statistical experiments defined by sums of N sample values for N → ∞ is analyzed.
Keywords: discrete Markov diffusion, evolutionary process, classification of equilibrium states, stochastic approximation.
1 Institute of Telecommunications and Global Information Space, National Academy of Sciences of Ukraine, Kyiv,
Ukraine,
e-mail: dimitri.koroliouk@ukr.net.
2 Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv,
Ukraine,
e-mail: vskorol@yahoo.com.