Search results for "Characteristic function"
showing 10 items of 26 documents
Stochastic dynamics of nonlinear systems with a fractional power-law nonlinear term: The fractional calculus approach
2011
Fractional power-law nonlinear drift arises in many applications of engineering interest, as in structures with nonlinear fluid viscous–elastic dampers. The probabilistic characterization of such structures under external Gaussian white noise excitation is still an open problem. This paper addresses the solution of such a nonlinear system providing the equation governing the evolution of the characteristic function, which involves the Riesz fractional operator. An efficient numerical procedure to handle the problem is also proposed.
Sur les problèmes d'optimisation structurelle
2000
We discuss existence theorems for shape optimization and material distribution problems. The conditions that we impose on the unknown sets are continuity of the boundary, respectively a certain measurability hypothesis. peerReviewed
Radon transform as a set of probability distributions
2009
It is proved that the Radon transform of the Wigner function gives the probability distributions related to measuring the observable operators obtained as linear combinations of position and momentum of the relevant particle. The generalization to an arbitrary number of degrees of freedom is given.
Stochastic analysis of external and parametric dynamical systems under sub-Gaussian Levy white-noise
2008
In this study stochastic analysis of non-linear dynamical systems under α-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of α-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with α/2- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function …
Riesz fractional integrals and complex fractional moments for the probabilistic characterization of random variables
2012
Abstract The aim of this paper is the probabilistic representation of the probability density function (PDF) or the characteristic function (CF) in terms of fractional moments of complex order. It is shown that such complex moments are related to Riesz and complementary Riesz integrals at the origin. By invoking the inverse Mellin transform theorem, the PDF or the CF is exactly evaluated in integral form in terms of complex fractional moments. Discretization leads to the conclusion that with few fractional moments the whole PDF or CF may be restored. Application to the pathological case of an α -stable random variable is discussed in detail, showing the impressive capability to characterize…
Limits in the characteristic function description of non-Lindblad-type open quantum systems
2005
In this paper I investigate the usability of the characteristic functions for the description of the dynamics of open quantum systems focussing on non-Lindblad-type master equations. I consider, as an example, a non-Markovian generalized master equation containing a memory kernel which may lead to nonphysical time evolutions characterized by negative values of the density matrix diagonal elements [S.M. Barnett and S. Stenholm, Phys. Rev. A {\bf 64}, 033808 (2001)]. The main result of the paper is to demonstrate that there exist situations in which the symmetrically ordered characteristic function is perfectly well defined while the corresponding density matrix loses positivity. Therefore no…
LÉVY FLIGHT SUPERDIFFUSION: AN INTRODUCTION
2008
After a short excursion from discovery of Brownian motion to the Richardson "law of four thirds" in turbulent diffusion, the article introduces the L\'{e}vy flight superdiffusion as a self-similar L\'{e}vy process. The condition of self-similarity converts the infinitely divisible characteristic function of the L\'{e}vy process into a stable characteristic function of the L\'{e}vy motion. The L\'{e}vy motion generalizes the Brownian motion on the base of the $\alpha$-stable distributions theory and fractional order derivatives. The further development of the idea lies on the generalization of the Langevin equation with a non-Gaussian white noise source and the use of functional approach. Th…
Mixed Convolutions and Zak Transforms
2015
In this chapter we introduce the mixed continuous–discrete and discrete–discrete convolutions. Important special cases of such convolutions are the polynomial and discrete splines, respectively. The Zak transforms, which are introduced in the chapter, provide integral representation of signals, which, in the following chapters, serves as a tool for the design of splines and spline-wavelets and operations over them. The exponential splines, which are the Zak transforms of polynomial and discrete B-splines are introduced. Explicit formulas for the characteristic functions of splines’ spaces are derived.
The norm of the characteristic function of a set in the John‐Nirenberg space of exponent p
2020
Stationary and non-stationary probability density function for non-linear oscillators
1997
A method for the evaluation of the stationary and non-stationary probability density function of non-linear oscillators subjected to random input is presented. The method requires the approximation of the probability density function of the response in terms of C-type Gram-Charlier series expansion. By applying the weighted residual method, the Fokker-Planck equation is reduced to a system of non-linear first order ordinary differential equations, where the unknowns are the coefficients of the series expansion. Furthermore, the relationships between the A-type and C-type Gram-Charlier series coefficient are derived.