Related papers: Some definite integrals arising from selfdecomposa…
There are characteristic classes that are the obstructions to the vanishing of the differentials in the Lyndon-Hochischild-Serre spectral sequence of an extension of an integral lattice L by a group G. These characteristic classes exist in…
This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We…
A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…
L\'evy's Upward Theorem says that the conditional expectation of an integrable random variable converges with probability one to its true value with increasing information. In this paper, we use methods from effective probability theory to…
Classes of multivariate and cone valued infinitely divisible Gamma distributions are introduced. Particular emphasis is put on the cone-valued case, due to the relevance of infinitely divisible distributions on the positive semi-definite…
Variable independence and decomposability are algorithmic techniques for simplifying logical formulas by tearing apart connections between free variables. These techniques were originally proposed to speed up query evaluation in constraint…
In this paper, we discuss the joint value distribution of $L$-functions in a suitable class. We obtain joint large deviations results in the central limit theorem for these $L$-functions and some mean value theorems, which give evidence…
In this paper, we present a comprehensive theory of generalized and weak generalized convolutions, illustrate it by a large number of examples, and discuss the related infinitely divisible distributions. We consider L\'{e}vy and additive…
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
Probabilistic programming provides the means to represent and reason about complex probabilistic models using programming language constructs. Even simple probabilistic programs can produce models with infinitely many variables. Factored…
Integrable probability has emerged as an active area of research at the interface of probability/mathematical physics/statistical mechanics on the one hand, and representation theory/integrable systems on the other. Informally, integrable…
We derive an identity that relates a class of multiple integrals involving Vandermonde polynomials to divided differences. Alternatively the identity can be viewed as an integral formula for divided differences. As part of the derivation we…
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…
Recent theoretical work on automatic differentiation (autodiff) has focused on characteristics such as correctness and efficiency while assuming that all derivatives are automatically generated by autodiff using program transformation, with…
Most integers are composite and most univariate polynomials over a finite field are reducible. The Prime Number Theorem and a classical result of Gau{\ss} count the remaining ones, approximately and exactly. For polynomials in two or more…
``Orderly divergence'' deals with limit theorems for weighted stochastic Gamma integrals of otherwise nonintegrable functions. Although for monotonic functions this category usually coincides with the classical notion of weighted limit…
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…
Copulas are essential tools in statistics and probability theory, enabling the study of the dependence structure between random variables independently of their marginal distributions. Among the various types of copulas, Ratio-Type Copulas…
The family of multivariate skew-normal distributions has many interesting properties. It is shown here that these hold for a general class of skew-elliptical distributions. For this class, several stochastic representations are established…
We extend the well-known Shannon decomposition of Boolean functions to more general classes of functions. Such decompositions, which we call pivotal decompositions, express the fact that every unary section of a function only depends upon…