Universal distribution function for the strongly-correlated fluctuations: General way for description of different random sequences

Abstract

It has been proved that for the strongly-correlated fluctuations there is a universal distribution function for the relative fluctuations (UDFRF). The analytical form of this function follows from the solution of some types of the functional equations. For obtaining the UDFRF a procedure of the optimal linear smoothing (POLS) has been developed. This procedure based on criterion of the minimal relative error helps to separate correctly a possible trend (the "low-frequency" curve, defined as the generalized mean value curve or trend) from the "high-frequency" (HF) fluctuations, defined as a random sequence of relative fluctuations with zero trend. A universal treatment procedure outlined in this paper helps to find an optimal trend, separate it from the relative HF fluctuations and read them quantitatively. The statistics of the fractional moments outlined in this paper helps "to read" the found trends and express them in terms of the fitting parameters if the model for their description is absent. These new possibilities can be applied for description of different noises (quantum fluctuations, for example) that always present on the scale (10-6 ÷ 10-9 m). Quantitative reading of these noises with their subsequent classification is important for every developing nanotechnology that it has a possibility to be applied in this range of scales. © 2009 Elsevier B.V. All rights reserved.