This note introduces shape orderings for stationary time series autocorrelation and partial autocorrelation functions and explores some of their convergence rate ramifications. The shapes explored include decreasing hazard rate and new better than used, orderings that are familiar from stochastic processes settings. Time series models where these shapes arise are presented. The shapes are used ...

We find the greatest values $alpha_{1} $ and $alpha_{2} $, and the least values $beta_{1} $ and $beta_{2} $ such that the inequalities $alpha_{1} C(a,b)+(1-alpha_{1} )H(a,b)

In this paper, a class of hybrid impulsive systems with time delays and stochastic effects are considered. We obtain some criteria on the global exponential stability in mean square for the impulsive stochastic delayed systems. To do this, differential inequalities and L-operator inequalities are developed. An example is given to illustrate the effectiveness of our results.

In this paper we explore some dynamic characteristics of the envelope of a bandpass Gaussian process, which are of interest in wireless fading channels. Specifically, we show that unlike the first derivative, the second derivative of the envelope, which appears in a number of applications, does not exist in the traditional mean square sense. However, we prove that the envelope is twice differen...

In this paper, we consider the problem of the mean-square optimal linear estimation of functionals which depend on the unknown values of a stationary stochastic sequence from observations with noise. In the case of spectral certainty in which the spectral densities of the sequences are exactly known, we propose formulas for calculating the spectral characteristic and value of the mean-square er...

The use of reduced basis has spread to many scientific fields for the last fifty years to condense the statistical properties of stochastic processes. Among these basis, the classical Karhunen-Loève basis corresponds to the Hilbertian basis that is constructed as the eigenfunctions of the covariance operator of the stochastic process of interest. The importance of this basis stems from its opti...

Study of soil properties like field capacity (F.C) and permanent wilting point (P.W.P) plays important roles in study of soil moisture retention curve. Pedotransfer functions (PTFs) provide an alternative by estimating soil parameters from more readily available soil data. In this study, a new approach is proposed as a modification to a standard fuzzy modeling method based on the table look-up ...

| Detection methods for multiple rate Direct Sequence Code Division Multiple Access (DS-CDMA) signalling are addressed. Attention is focussed on the development of receivers based on the minimum mean squared error (MMSE). Due to the cyclostationarity of the mul-tirate signal, a representation of the multirate signal in terms of the Fourier basis is possible. This expansion facilitates construct...