相关论文: Free self-decomposability and unimodality of the F…

A probability distribution $\mu$ on $\mathbb{R}^d$ is quasi-infinitely divisible if its characteristic function has the representation $\widehat{\mu} = \widehat{\mu_1}/\widehat{\mu_2}$ with infinitely divisible distributions $\mu_1$ and…

We consider distributions on $\mathbb{R}$ that can be written as the sum of a non-zero discrete distribution and an absolutely continuous distribution. We show that such a distribution is quasi-infinitely divisible if and only if its…

In this note we consider the Hausdorff dimension of self-affine sets with random perturbations. We extend previous work in this area by allowing the random perturbation to be distributed according to distributions with unbounded support as…

Properties of the law $\mu$ of the integral $\int_0^{\infty}c^{-N_{t-}}\,dY_t$ are studied, where $c>1$ and $\{(N_t,Y_t),t\geq0\}$ is a bivariate L\'{e}vy process such that $\{N_t\}$ and $\{Y_t\}$ are Poisson processes with parameters $a$…

We introduce an interesting method of proving separable reduction theorems - the method of elementary submodels. We are studying whether it is true that a set (function) has given property if and only if it has this property with respect to…

We consider nonnegative r-potent matrices with finite dimensions and study their decomposability. We derive the precise conditions under which an r-potent matrix is decomposable. We further determine a general structure for the r-potent…

Within the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard…

We prove that the distribution of the product of two correlated normal random variables with arbitrary means and arbitrary variances is infinitely divisible. We also obtain exact formulas for the probability density function of the sum of…

The purpose of this paper is to study and classify singular solutions of the Poisson problem $$ %\begin{equation}\label{eq 0.1} \left \{ \begin{aligned} {\mathcal L}^s_\mu u = f \quad\ {\rm in}\ \, \Omega\setminus \{0\},\\ u =0 \quad\ {\rm…

Let $u$ be a non-negative super-solution to a $1$-dimensional singular parabolic equation of $p$-Laplacian type ($1<p<2$). If $u$ is bounded below on a time-segment $\{y\}\times(0,T]$ by a positive number $M$, then it has a power-like decay…

We define Letac-Wesolowski-Matsumoto-Yor (LWMY) functions as decreasing functions from $(0,\infty)$ onto $(0,\infty)$ with the following property: there exist independent, positive random variables $X$ and $Y$ such that the variables…

Inspired by R. Speicher's multidimensional free central limit theorem and semicircle families, we prove an infinite dimensional compound Poisson limit theorem in free probability, and define infinite dimensional compound free Poisson…

We calculate the almost sure Hausdorff dimension of uniformly random self-similar fractals. These random fractals are generated from a finite family of similarities, where the linear parts of the mappings are independent uniformly…

In the present article, topological, metric, and fractal properties of certain sets are investigated. These sets are images of sets whose elements have restrictions on using digits or combinations of digits in own s-adic representations,…

Given a parabolic cylinder $Q =(0,T)\times\Omega$, where $\Omega\subset \mathbb{R}^{N}$ is a bounded domain, we prove new properties of solutions of \[ u_t-\Delta_p u = \mu \quad \text{in $Q$} \] with Dirichlet boundary conditions, where…

Let $C_n$ be the $n$th Catalan number. We show that the asymptotic density of the set $\{n: C_n \equiv 0 \mod p \}$ is $1$ for all primes $p$, We also show that if $n = p^k -1$ then $C_n \equiv -1 \mod p$. Finally we show that if $n \equiv…

We study fragmentation equations with power-law fragmentation rates and polynomial daughter fragments distribution function $p(s)$. The corresponding selfsimillar solutions are analysed and their exponentially decaying asymptotic behaviour…

We give a simple proof of a fairly flexible comparison theorem for equations of the type $-(p(u'+su))'+rp(u'+su)+qu=0$ on a finite interval where $1/p$, $r$, $s$, and $q$ are real and integrable. Flexibility is provided by two functions…

We prove three theorems concerning the Hopf-Galois module structure of fractional ideals in a finite tamely ramified extension of $ p $-adic fields or number fields which is $ H $-Galois for a commutative Hopf algebra $ H $. Firstly, we…

It is well known that sets of $p$-capacity zero are removable for bounded $p$-harmonic functions, but on metric spaces there are examples of removable sets of positive capacity. In this paper, we show that this can happen even on unweighted…