Search results for "Generalized Taylor Serie"
showing 3 items of 3 documents
On the use of fractional calculus for the probabilistic characterization of random variables
2009
In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the characteristic function (CF). The CF can be further expressed by a Taylor series involving the moments of the random variable. However, in some circumstances, the moments do not exist and the Taylor expansion of the CF is useless. This happens for example in the case of $\alpha$--stable random variables. Here, the problem of representing the CF or the PDF of random variables (r.vs) is examined by introducing fractional calculus. Two very remarkable results are o…
A representation of wind velocity by means of fractional spectral moments
2009
This paper deals with the definition of a new function that is a link between Power Spectral Density (PSD) and correlation function, called the Fractional Spectral Moments function. This is defined as the moment of complex order g of the one-sided PSD. It is shown that by means of this complex function both the correlation function and PSD can be represented with great accuracy.
A new representation of power spectral density and correlation function by means of fractional spectral moments
2009
In this paper, a new perspective for the representation of both the power spectral density and the correlation function by a unique class of function is introduced. We define the moments of order gamma (gamma being a complex number) of the one sided power spectral density and we call them Fractional Spectral Moments (FSM). These complex quantities remain finite also in the case in which the ordinary spectral moments diverge, and are able to represent the whole Power Spectral Density and the corresponding correlation function.