Binary statistical experiments with persistent nonlinear regression

Abstract

A sequence of binary stochastic experiments with persistent nonlinear regression is considered. The regression is defined as a product of a linear directed force and nonlinear term changing the directed force in a neighborhood of boundary points. A stochastic approximation for the sequence of stationary experiments is constructed with the help of an autoregressive process with normal perturbation. A stochastic approximation of the sequence of exponential stochastic experiments is also constructed with the help of an exponential autoregressive process.

Filtering of stationary Gaussian statistical experiments

“…Namely, some natural conditions [3,Proposition 5.2], the SE (1) has the following diffusion approximation:…”

Dynamics of ternary statistical experiments with equilibrium state

“…The dynamics of SE characteristics is determined by a linear regression function [2] which specifies the values of SE characteristics in the next stage of observation, for given value probability at the present stage.…”

“…In the works [1], [2], [3], [4], [5] a model of binary statistical experiments with persistent regression and equilibrium is considered for several aspects of investigation. The present work considers the ternary model in a three-dimensional scheme of discrete stationary Markov diffusion, defined by a vector difference stochastic equation.…”

Differential diffusion model with two equilibrium states

“…In our works [1,2] we research statistical experiments (SE), given by the average sums of sample values that take binary values. The corresponding SE frequencies are set by the average sums:…”