The forward estimation problem for stationary and ergodic time series {X n } ∞ n=0 taking values from a finite alphabet X is to estimate the probability that X n+1 = x based on the observations X i , 0 ≤ i ≤ n without prior knowledge of the distribution of the process {X n }. We present a simple procedure g n which is evaluated on the data)| → 0 almost surely for a subclass of all stationary an...

In the present study, we construct a new matrix which call quasi-Cesaro and is generalization of ordinary Cesaro matrix, introduce $BK$-spaces $C^q_k$ $C^q_{\infty}$ as domain $C^q$ in spaces $\ell_k$ $\ell_{\infty},$ respectively. Furthermore, exhibit some topological properties inclusion relations related to these newly defined spaces. We determine basis space obtain Köthe duals $C^q_{\infty}...

Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of a μ-almost equicontinuous cellular automata F , converges in Cesaro mean to an invariant measure μc. If the initial measure μ is a Bernouilli measure, we prove that the Cesaro mean limit measure μc is shift mixing. ...

We study the asymptotic behavior of random time changes dynamical systems. As we propose three classes which exhibits different patterns decays. The subordination principle may be applied to It turns out that for special case stable subordinators explicit expressions are known and its derived. For more general calculations essentially complicated reduce our corresponding Cesaro limit.

We consider a porous thermoelastic body, including voidage time derivative among the independent constitutive variables. For the initial boundary value problem of such materials, we analyze the temporal behaviour of the solutions. To this aim we use the Cesaro means for the components of energy and prove the asymptotic equipartition in mean of the kinetic and strain energies.