Let {(Xi, Yi)} be a stationary ergodic time series with (X, Y ) values in the product space R ⊗ R. This study offers what is believed to be the first strongly consistent (with respect to pointwise, least-squares, and uniform distance) algorithm for inferring m(x) = E[Y0|X0 = x] under the presumption that m(x) is uniformly Lipschitz continuous. Autoregression, or forecasting, is an important spe...

We present a construction showing that a class of sets C that is Glivenko-Cantelli for an i.i.d. process need not be Glivenko-Cantelli for every stationary ergodic process with the same one dimensional marginal distribution. This result provides a counterpoint to recent work extending uniform strong laws to ergodic processes, and a recent characterization of universal Glivenko Cantelli classes.

When is a nonlinear filter stable with respect to its initial condition? In spite of the recent progress, this question still lacks a complete answer in general. Currently available results indicate that stability of the filter depends on the signal ergodic properties and the observation process regularity and may fail if either of the ingredients is ignored. In this note we address the questio...

We study the relative impact of small-scale random inhomogeneities and singular perturbations in nonlinear elasticity. More precisely, we analyse the asymptotic behaviour of the energy functionals Fε(ω)(u) = ∫ A ( f ( ω, x ε ,Du ) + ε|∆u| ) dx, where ω is a random parameter and ε > 0 denotes a typical length-scale associated with the variations in the elastic properties of the body. For f stati...

Consider the Wonham optimal ltering problem for a nite state ergodic Markov process in both discrete and continuous time, and let be the noise intensity for the observation. We examine the sensitivity of the solution with respect to the lter's initial conditions in terms of the gap between the rst two Lyapunov exponents of the Zakai equation for the unnormalized conditional probability. This ga...

A novel ergodic cellular automaton model of gene-protein network is presented. It shown that the presented can predict occurrences typical nonlinear phenomena a conventional ordinary differential equation model. In addition, theoretical analysis methods are proposed. Using methods, an important advantage revealed: better suited to compared regular (standard) automaton. Furthermore, implemented ...

We construct ergodic actions of compact quantum groups on C∗-algebras and von Neumann algebras, and exhibit phenomena of such actions that are of different nature from ergodic actions of compact groups. In particular, we construct: (1). an ergodic action of the compact quantum Au(Q) on the type IIIλ Powers factor Rλ for an appropriate positive Q ∈ GL(2, R); (2). an ergodic action of the compact...

Typical approaches to acoustic echo cancellation (AEC) in mobile telephones employ adaptive linear algorithms, such as the normalized least mean squares (NLMS) algorithm. Smaller, cheaper components on these devices introduce nonlinearities into the echo path, which adversely affect performance of linear AEC systems and necessitate means of nonlinear compensation. Memoryless nonlinear blocks th...