Related papers: Fractional Wiener Chaos
Many generalizations of continued fractions, where the reciprocal function has been replaced by a more general function, have been studied, and it is often asked whether such generalized expansions can have nice properties. For instance, we…
Fractal geometry and analysis constitute a growing field, with numerous applications, based on the principles of fractional calculus. Fractals sets are highly effective in improving convex inequalities and their generalisations. In this…
A power expansion scheme is set up to determine the Wigner function that satisfies the quantum kinetic equation for spin-1/2 charged fermions in a background electromagnetic field. Vector and axial-vector current induced by magnetic field…
We compute all massive partition functions or characteristic polynomials and their complex eigenvalue correlation functions for non-Hermitean extensions of the symplectic and chiral symplectic ensemble of random matrices. Our results are…
The recently introduced basis adaptation method for Homogeneous (Wiener) Chaos expansions is explored in a new context where the rotation/projection matrices are computed by discovering the active subspace where the random input exhibits…
The operational calculus associated with special polynomials has proven to be a powerful tool for analyzing and simplifying their properties. This article examines the bivariate degenerate Hermite polynomials with a focus on their…
Assuming that both a function and its Fourier transform are dominated by a Gaussian of large variance, it is shown that the Hermite coefficients of the function decay exponentially. A sharp estimate for the rate of exponential decay is…
In this paper, we simulate diffusion bridges by using an approximation of the Wiener-chaos expansion (WCE), or a Fourier-Hermite expansion, for a related diffusion process. Indeed, we consider the solution of stochastic differential…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn to try extending our reach to include quaternions. The non-commutativity of the quaternion algebra poses…
We calculate the Fourier transform of a spherically symmetric exponential function. Our evaluation is much simpler than the known one. We use the polar coordinates and reduce the Fourier transform to the integral of a rational function of…
We propose a phase-space representation concept in terms of the Wigner function for a quantum harmonic oscillator model that exhibits the semiconfinement effect through its mass varying with the position. The new method is used to compute…
Hermite polynomials, which are associated to a Gaussian weight and solve the Laplace equation with a drift term of linear growth, are classical in analysis and well-understood via ODE techniques. Our main contribution is to give explicit…
We compute Hermite expansions of some tempered distributions by using the Bargmann transform. In other words, we calculate the Taylor expansions of the corresponding entire functions. Our method of computations seems to be superior to the…
Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel…
In this paper, we consider a quaternionic short-time Fourier transform (QSTFT) with normalized Hermite functions as windows. It turns out that such a transform is based on the recent theory of slice polyanalytic functions on quaternions.…
In this article we replace the semi-heuristic derivation of the Rosenfeld functional of hard convex particles with the systematic calculation of Mayer clusters. It is shown that each cluster integral further decomposes into diagrams of…
Many different types of fractional calculus have been defined, which may be categorised into broad classes according to their properties and behaviours. Two types that have been much studied in the literature are the Hadamard-type…
We consider a modified quadratic variation of the Hermite process based on some well-chosen increments of this process. These special increments have the very useful property to be independent and identically distributed up to…
The classical binomial process has been studied by \citet{jakeman} (and the references therein) and has been used to characterize a series of radiation states in quantum optics. In particular, he studied a classical birth-death process…