Related papers: Convolvability and regularization of distributions

The coupled Maxwell-Lorentz system describes feed-back action of electromagnetic fields in classical electrodynamics. When applied to point-charge sources (viewed as limiting cases of charged fluids) the resulting nonlinear weakly…

We provide a new proof of Alesker's Irreducibility Theorem. We first introduce a new localization technique for polynomial valuations on convex bodies, which we use to independently prove that smooth and translation invariant valuations are…

Let ($X,Y)$ be a random vector with distribution function $F(x,y),$ and $(X_{1},Y_{1}),(X_{2},Y_{2}),...,(X_{n},Y_{n})$ are independent copies of ($X,Y).$ Let $X_{i:n}$ be the $i$th order statistics constructed from the sample…

A closed set of \textit{exact} equations describing statistical theory of turbulent self-diffusion by multivariate-normal turbulent velocity field is derived. In doing so, we first suggest exact formulas for correlations…

The mollified uniform distribution is rediscovered, which constitutes a ``soft'' version of the continuous uniform distribution. Important stochastic properties are presented and used to demonstrate potential fields of applications. For…

Azzalini & Dalla Valle (1996) have recently discussed the multivariate skew-normal distribution which extends the class of normal distributions by the addition of a shape parameter. The first part of the present paper examines further…

A probability distribution is n-divisible if its nth convolution root exists. While modeling the dependence structure between several (re)insurance losses by an additive risk factor model, the infinite divisibility, that is the…

The conflation of a finite number of probability distributions P_1,..., P_n is a consolidation of those distributions into a single probability distribution Q=Q(P_1,..., P_n), where intuitively Q is the conditional distribution of…

For a probability P in $R^d$ its center outward distribution function $F_{\pm}$, introduced in Chernozhukov et al. (2017) and Hallin et al. (2021), is a new and successful concept of multivariate distribution function based on mass…

Three-way data can be conveniently modelled by using matrix variate distributions. Although there has been a lot of work for the matrix variate normal distribution, there is little work in the area of matrix skew distributions. Three matrix…

In this article, we explore convolutions of distributions with distributions given by (weighted) line integration. We also explore the scattering of singularities of such convolutions.

Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…

Probability distribution theory helps in studying the impact of various dimensions in life while the Mittag-Leffler function and bicomplex are used in electromagnetism, quantum mechanics, and signal theory. Considering the importance of…

It is shown that Euclidean field theory with polynomial interaction, can be regularized using the wavelet representation of the fields. The connections between wavelet based regularization and stochastic quantization are considered.

In this note we provide a quick proof of the Sklar's Theorem on the existence of copulas by using the generalized inverse functions as in the one dimensional case, but a little more sophisticated.

Here we give a definition of regularity on multiprojective spaces which is different from the definitions of Hoffmann-Wang and Costa-Mir\'o Roig. By using this notion we prove some splitting criteria for vector bundles.

This is the fourth part in the series of articles math.MG/0503397, math.MG/0503399, math.MG/0509512 where the theory of valuations on manifolds is developed. In this part it is shown that the filtration on valuations introduced in…

These notes briefly consider convolutions of tempered distributions with functions in the Schwartz class.

Majorization theory is a powerful mathematical tool to compare the disorder in distributions, with wide-ranging applications in many fields including mathematics, physics, information theory, and economics. While majorization theory…

In this paper we give a first attempt to define and study stable distributions with respect to the weak generalized convolution, focusing our attention on the symmetric weakly stable distribution. As in the case of the classical…