Arguments have been provided against the use of the eigenvector as the operator that derives priorities. A highlight of the arguments is that the eigenvector solution does not always respect the condition of ordinal preference (COP) based on the decision maker’s judgments. While this condition may be reasonable when dealing with measurable concepts (such as distance or time) that lead to consis...

We prove that a stationary max–infinitely divisible process is mixing (ergodic) iff its dependence function converges to 0 (is Cesaro summable to 0). These criteria are applied to some classes of max–infinitely divisible processes.

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. ...

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 such automata 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. Therefore we also show that for an...

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...

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.