Related papers: Closure properties in positively decreasing and re…
In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
Weak convergence of maxima of dependent sequences of identically distributed continuous random variables is studied under normalizing sequences arising as subsequences of the normalizing sequences from an associated iid sequence. This…
By a closure space we will mean a pair $(A,\mathcal{C})$, in which $A$ is a set and $\mathcal{C}$ a set of subsets of $A$ closed under arbitrary intersections. The purpose of this paper is to initiate a development of descent theory of…
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…
We investigate closure operators and describe their properties for $E$-combinations and $P$-combinations of structures and their theories. We prove, for $E$-combinations, that the existence of a minimal generating set of theories is…
We study a new class of so-called rational-infinitely (or quasi-infinitely) divisible probability laws on the real line. The characteristic functions of these distributions are ratios of the characteristic functions of classical infinitely…
We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…
Truncated multivariate distributions arise extensively in econometric modelling when non-negative random variables are intrinsic to the data-generation process. More broadly, truncated multivariate distributions have appeared in censored…
Many Properties of a category X, as for instance the existence of an adjoint or a factorization system, are a consequence of the cowellpoweredness of X. In the absence of cowellpoweredness, for general results, fairly strong assumption on…
We describe a new class of positive linear discrete-time switching systems for which the problems of stability or stabilizability can be resolved constructively. This class generalizes the class of systems with independently switching state…
Strong negative dependence properties have recently been proved for the symmetric exclusion process. In this paper, we apply these results to prove convergence to the Poisson and normal distributions for various functionals of the process.
We study the preservation of certain properties under products of classes of finite structures. In particular, we examine indivisibility, definable self-similarity, the amalgamation property, and the disjoint n-amalgamation property. We…
We consider the canonical pseudodistributive law between various free limit completion pseudomonads and the free coproduct completion pseudomonad. When the class of limits includes pullbacks, we show that this consideration leads to notions…
We determine all functional closure properties of finite $\mathbb{N}$-weighted automata, even all multivariate ones, and in particular all multivariate polynomials. We also determine all univariate closure properties in the promise setting,…
A folklore result in category theory is that a (weakly) Cartesian closed category with finite co-products is distributive. Usually, the proof of this small result is carried on using the fact that the exponential functor is right adjoint to…
This paper develops a more general theory of sequences of dependent categorical random variables, extending the works of Korzeniowski (2013) and Traylor (2017) that studied first-kind dependency in sequences of Bernoulli and categorical…
Positive dependencies have been compared in the literature under rather strong assumptions such as equality of conditional distributions, exchangeability, or stationarity. We establish supermodular ordering results for distributions that…
In the probability theory limit distributions (or probability measures) are often characterized by some convolution equations (factorization properties) rather than by Fourier transforms (the characteristic functionals). In fact, usually…
In this paper we introduce several natural definitions of asymptotic independence of two sequences of random elements. We discuss their basic properties, some simple connections between them and connections with properties of weak…