non-Gaussian Time Series Research Articles

Estimation of coherence spectrum of non-Gaussian time series populations

Previous work on computation of coherence estimates between two time series and the confidence intervals about these estimates has always assumed that the time series have a Gaussian probability density function. Here a Monte Carlo study was performed, computing coherences and confidence intervals upon non-Gaussian time series. Using both a rectangular distribution and a x <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> distribution with one degree of freedom, the results appear to justify the notion that the assumption of a Gaussian distribution has a fairly small importance in the computation of the above statistics.

Fractional Brownian Motions, Fractional Noises and Applications

Fractional Brownian Motions, Fractional Noises and Applications

A Study on the Statistical Synthesis of Optimum Nonlinear Control Systems Subjected to Non-Gaussian Random Inputs

In this paper, a practical synthesizing technique, in the statistical sense, of the optimum nonlinear control system subjected to non-Gaussian random inputs is presented. The technique described here is a method of circumventing difficulties of mathematical treatment. The description begins with the construction of the optimum nonlinear filter under the excitation of non-Gaussian time series. It is analytically shown that the optimum nonlinear filter consists of a nonlinear element of zero-memory type sandwitched between two linear filters. By applying these results to the synthesis of feedback control systems with a random signal in the presense of non-Gaussian random noise, the optimum control system containing a nonlinear element is derived. Detailed descriptions of these synthesizing procedures are illustrated by several examples.