Related papers: On weak generalized stability and (c,d)-pseudostab…
A random vector ${\bf X}$ is weakly stable iff for all $a,b\in \mathbb{R}$ there exists a random variable $\Theta$ such that $a{\bf X}+b{\bf X}'\stackrel{d}{=}{\bf X}\Theta$. This is equivalent (see \cite{MOU}) with the condition that for…
A random vector ${\bf X}$ is weakly stable iff for all $a,b \in \mathbb{R}$ there exists a random variable $\Theta$ such that $a{\bf X} + b {\bf X}' \stackrel{d}{=} {\bf X} \Theta$, where $X'$ is an independent copy of $X$ and $\Theta$ is…
The explicit form for the characteristic function of a stable distribution on the line is derived analytically by solving the associated functional equation and applying theory of regular variation, without appeal to the general…
We introduce the notion of symmetric covariation, which is a new measure of dependence between two components of a symmetric $\alpha$-stable random vector, where the stability parameter $\alpha$ measures the heavy-tailedness of its…
We investigate a family of distributions having a property of stability-under-addition, provided that the number $\nu$ of added-up random variables in the random sum is also a random variable. We call the corresponding property a…
In this paper, weakly homogeneous generalized functions in the special Colombeau algebras are determined up to equality in the sense of generalized distributions. This yields characterizations that are formally similar to distribution…
We introduce a class of distributions originating from an exponential family and having a property related to the strict stability property. A characteristic function representation for this family is obtained and its properties are…
Doubly nonlinear stochastic evolution equations are considered. Upon assuming the additive noise to be rough enough, we prove the existence of probabilistically weak solutions of Friedrichs type and study their uniqueness in law. This…
Here we introduce some new classes of discrete stable random variables, which are useful for understanding of a new general notion of stability of random variables called us as casual stability. There are given some examples of casual and…
We study p-adic counterparts of stable distributions, that is limit distributions for sequences of normalized sums of independent identically distributed p-adic-valued random variables. In contrast to the classical case, non-degenerate…
Convolutions of long-tailed and subexponential distributions play a major role in the analysis of many stochastic systems. We study these convolutions, proving some important new results through a simple and coherent approach, and showing…
We investigate linear parabolic equations in divergence form with singular coefficients and non-smooth boundary data. When the diffusion, drift, or potential terms, as well as the initial or boundary conditions, are distributions rather…
Very recently we present a theory to discuss the nature of light and show that the quantization of light energy in vacuum can be derived directly from classical electromagnetic theory. In the theory a key concept of stability of statistical…
In this paper, we study properties and patterns on permutations of multisets whose multivariate generating functions are symmetric. We interpret this phenomenon through the lens of group actions and define such a property or pattern as…
Due to the existence of multiple stationary distributions, we study the stability and instability of a stationary distribution for distribution dependent stochastic differential equations. This note is devoted to the instability of a…
We discuss recently developed methods that quantify the stability and generalizability of statistical findings under distributional changes. In many practical problems, the data is not drawn i.i.d. from the target population. For example,…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
In this paper we define the closure under weak convergence of the class of p-tempered {\alpha}-stable distributions. We give necessary and sufficient conditions for convergence of sequences in this class. Moreover, we show that any element…
This article deals with different generalizations of the discrete stability property. Three possible definitions of discrete stability are introduced, followed by a study of some particular cases of discrete stable distributions and their…