Related papers: On the integral modulus of infinitely divisible di…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
We study the density of the invariant measure of the Hurwitz complex continued fraction from a computational perspective. It is known that this density is piece-wise real-analytic and so we provide a method for calculating the Taylor…
We consider impulsive dynamical systems defined on compact metric spaces and their respective impulsive semiflows. We establish sufficient conditions for the existence of probability measures which are invariant by such impulsive semiflows.…
We propose a new discretization of the mirror-Langevin diffusion and give a crisp proof of its convergence. Our analysis uses relative convexity/smoothness and self-concordance, ideas which originated in convex optimization, together with a…
We describe basic motivations behind quantum or noncommutative probability, introduce quantum L\'evy processes on compact quantum groups, and discuss several aspects of the study of the latter in the example of quantum permutation groups.…
An infinitely divisible distribution on $\mathbb{R}$ is a probability measure $\mu$ such that the characteristic function $\hat{\mu}$ has a L\'{e}vy-Khintchine representation with characteristic triplet $(a,\gamma, \nu)$, where $\nu$ is a…
For various classes of Lipschitz functions we provide dimension free concentration inequalities for infinitely divisible random vectors with independent components and finite exponential moments.
Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and machine learning. We look at programming language models for imprecise probability. Our…
This article presents some interesting and novel results concerning the average modulus of random polynomials on the unit circle and the unit disc, with coefficients distributed as standard normal variates. The paper also introduces new…
The one-dimensional Dickman distribution arises in various stochastic models across number theory, combinatorics, physics, and biology. Recently, a definition of the multidimensional Dickman distribution has appeared in the literature,…
We consider distributions of ordered random vectors with given one-dimensional marginal distributions. We give an elementary necessary and sufficient condition for the existence of such a distribution with finite entropy. In this case, we…
We study in this paper the sufficient conditions for enhanced continuity of random fields, i.e. such that the modulus of its continuity allows the factorable representation by the product of random variable on the deterministic module of…
Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has…
We introduce a probability distribution Q on the group of permutations of the set Z of integers. Distribution Q is a natural extension of the Mallows distribution on the finite symmetric group. A one-sided infinite counterpart of Q,…
We compute the limit distribution of partial transposes (when both the number and the size of blocks tends to infinity) for a large class of ensembles of unitarily invariant random matrices. Furthermore, it is shown the asymptotic freeness…
In this work we first introduce quasi-infinitely divisible (QID) random measures and formulate spectral representations. Then, we introduce QID stochastic integrals and present integrability conditions and continuity properties. Further, we…
Methods for generating new distributions from old can be thought of as techniques for simplifying integrals used in reverse. Hence integrating a probability density function (pdf) by parts provides a new way of modifying distributions; the…
Random integral mappings $I^{h,r}_{(a,b]}$ give isomorphisms between the sub-semigroups of the classical $(ID, \ast)$ and the free-infinite divisible $(ID,\boxplus)$ probability measures. This allows us to introduce new examples of such…
We determine the probability distribution for the field inside a random uniform distribution of electric or magnetic dipoles. For parallel dipoles, simulations and an analytical derivation show that although the average contribution from…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…