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… (More)

Many scientific studies require a thorough understanding of the scaling characteristics of observed processes. We derive and justify a decomposition of the usual cross-covariance in terms of scale-by-scale wavelet cross-covariances, and describe estimators of both quantities along with asymptotic equivalences. The scale-by-scale decomposition of… (More)

This letter describes the implementation of second-order one-way wave-equation absorbing boundary conditions (ABCs) in two unconditionally stable finite-difference time-domain (FDTD) methods-namely the locally one-dimensional (LOD)- and the alternating-direction implicit (ADI)-FDTD methods. The Higdon second-order absorbing operator is discretized in the… (More)

In recent years, split-step finite-difference time-domain (SS-FDTD) methods have attracted much attention and many implementations have been developed to improve their accuracy and efficiency. In this communication the equivalence between some of these recently reported techniques and conventional schemes is shown. More specifically, we prove that there are… (More)