In this paper, we construct an analog of local time for arbitrary Lévy process with finite second moment. When our is a Wiener process, object coincides the time.

For time-invariant degradation models and stationary signals and noise, the classical Fourier domain Wiener filter, which can be implemented in O(N logN) time, gives the minimum mean-square-error estimate of the original undistorted signal. For time-varying degradations and nonstationary processes, however, the optimal linear estimate requires O(N2) time for implementation. We consider filterin...

Fix ν > 0, denote by G(ν/2) a Gamma random variable with parameter ν/2 and let n ≥ 2 be a fixed even integer. Consider a sequence {F k } k≥1 of square integrable random variables belonging to the nth Wiener chaos of a given Gaussian process and with variance converging to 2ν. As k → ∞, we prove that F k converges in distribution to 2G(ν/2) − ν if and only if E(F 4 k) − 12E(F 3 k) → 12ν 2 − 48ν.

We consider the class of all the Hermite processes (Z t )t2[0;1] of order q 2 N and with Hurst index H 2 ( 1 2 ; 1). The process Z (q;H) is H-self-similar, it has stationary increments and it exhibits long-range dependence identical to that of fractional Brownian motion (fBm). For q = 1, Z is fBm, which is Gaussian; for q = 2, Z is the Rosenblatt process, which lives in the second Wiener chaos;...

In 1959 Chernoff [7] initiated the study of the asymptotic theory of sequential Bayes tests as the cost of observation tends to zero. He dealt with the case of a finite parameter space. The definitive generalization of the line of attack initiated in that paper was given by Kiefer and Sacks in [13]. Their work as well as that of Chernoff, the intervening papers of Albert [1], Bessler [3], and S...

In this paper, firstly, one deals with the stability and the stabilizability problems for the class of Markovian jump continuous-time singular systems. Next, one will address the robustness problem. The proposed approaches derive sufficient conditions such that the regularity and the absence of impulses are assured as well as the stochastic stability and robust stochastic stability. Also, state...

Accelerated degradation testing (ADT) is an efficient tool to conduct material service reliability and safety evaluations by analyzing performance degradation data. Traditional stochastic process models are mainly for linear or linearization degradation paths. However, those methods are not applicable for the situations where the degradation processes cannot be linearized. Hence, in this paper,...

The Wiener index of a connected graph G, denoted by W(G) , is defined as ∑ ( , ) , ∈ ( ) .Similarly, hyper-Wiener index of a connected graph G,denoted by WW(G), is defined as ( ) + ∑ ( , ) , ∈ ( ) .In this paper, we present the explicit formulae for the Wiener, hyper-Wiener and reverse Wiener indices of some graph operations. Using the results obtained here, the exact formulae for Wiener, hyper...

The multistage Wiener filter (MWF) outperforms the full rank Wiener filter in low sample support environments. However, the MWF adaptive process should be stopped at an optimum stage to get the best performance. There are two methods to stop the MWF adaptive process. One method is to calculate until the final full-stage, and the second method is to terminate at r-stage less than full-stage. The...

Consider the three-component time series model that decomposes observed data (Y ) into the sum of seasonal (S), trend (T ), and irregular (I) portions. Assuming that S and T are nonstationary and that I is stationary, it is demonstrated that widely-used Wiener-Kolmogorov signal extraction estimates of S and T can be obtained through an iteration scheme applied to optimal estimates derived from ...