Two component binary statistical experiments with persistent linear regression

Filtering of stationary Gaussian statistical experiments

“…In this case, the random amount S N (k), k ≥ 0, describes the relative frequencies of presence of the attribute A in a sample of fixed volume N at each time instant k ≥ 0. Introducing the normalized fluctuations ζ N (k) := √ N(S N (k) − ρ), where ρ be the equilibrium of SE [1,2], one gets an important representation of SEs.…”

Binary statistical experiments with persistent nonlinear regression

“…In the current paper, the regression function of increments is given by the product of two components, namely of the linear directed force [V − p − − V + p + ] defined in [1] and the factor p + p − that changes the directed force in a neighborhood of boundary values −1 and +1. Such a nonlinear factor appears, for example, in the Wright-Fisher model (see, for example, [2, Chapter 10]).…”

“…According to ( 1)-( 5), it is sufficient to prove either the convergence of stochastic experiments (1) or that of one of their frequency components (2). Below we prove the convergence of stochastic experiments (1).…”

“…The preceding paper [1] is devoted to the study of the asymptotic behavior of stochastic experiments constructed with the help of a linear regression function of the increments.…”

“…In the current paper, the directed forces (see [1,Assumption]) include a nonlinear factor and this makes the asymptotic analysis of stochastic experiments much more complicated. At the same time, only the variance of the normal autoregressive process is influenced by the nonlinear component (see [1,Proposition 5.1]).…”