Covariances of Zero Crossings in Gaussian Processes

On the average number of sharp crossings of certain Gaussian random polynomials

Estimation of Fractal Index and Fractal Dimension of a Gaussian Process by Counting the Number of Level Crossings

The fractal index (Y and fractal dimension D of a Gaussian process are characteristics that describe the smoothness of the process. In principle, smoother processes have fewer crossings of a given level, and so level crossings might be employed to estimate (Y or D. However, the number of crossings of a level by a non-differentiable Gaussian process is either zero or infinity, with probability o...

Complete convergence of moving-average processes under negative dependence sub-Gaussian assumptions

The complete convergence is investigated for moving-average processes of doubly infinite sequence of negative dependence sub-gaussian random variables with zero means, finite variances and absolutely summable coefficients. As a corollary, the rate of complete convergence is obtained under some suitable conditions on the coefficients.

Wavelet Scale Analysis of Bivariate Time Series II: Statistical Properties for Linear Processes

Scaling characteristics of stochastic processes can be examined using wavelet cross-covariances. For jointly stationary but generally non-Gaussian linear processes, the asymptotic properties of the resulting wavelet cross-covariance estimator are derived. The linear processes are assumed to have only a square-summable weight sequence, so that the class of processes includes long-memory processe...

Gaussian Measures in Function Space

Two Gaussian measures are either mutually singular or equivalent. This dichotomy was first discovered by Feldman and Hajek (independently). We give a simple, almost formal, proof of this result, based on the study of a certain pair of functionals of the two measures. In addition we show that two Gaussian measures with zero means and smooth Polya-type covariances (on an interval) are equivalent ...