Related papers: The moment problem for random objects in a categor…
Let $\mu$ be a probability measure (or corresponding random variable) such that all moments $\mu_n$ exist. Knowledge of the moments is not sufficient to determine infinite divisibility of the measure; we show also that infinitely divisible,…
A goodness-of-fit test for one-parameter count distributions with finite second moment is proposed. The test statistic is derived from the $L^1$ distance of a function of the probability generating function of the model under the null…
We study the general moment problem for measures on the real line, with polynomials replaced by more general spaces of entire functions. As a particular case, we describe measures that are uniquely determined by a restriction of their…
We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…
The goal of this paper is to prove theorems that elucidate the Cohen-Lenstra-Martinet conjectures for the distributions of class groups of number fields, and further the understanding of their implications. We start by giving a simpler…
We have analyzed some conditions which are essentially involved in deciding whether or not a probability distribution is unique (moment-determinate) or non-unique (moment-indeterminate) by its moments. We suggest new conditions concerning…
The conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables, a prominent example being instrumental variable regression. A standard approach reduces the problem to a finite…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…
The Stieltjes classes play a significant role in the moment problem since they permit to expose an infinite family of probability distributions all having equal moments of all orders. Given a moment-indeterminate distribution, it may not be…
We recall the definition and the properties of a moment sequence and recall that all real sequences that have a finite rank of its Hankel matrix (see definition in the sequel) satisfy a homogeneous linear equation with constant…
Generalized moment problems optimize functional expectation over a class of distributions with generalized moment constraints, i.e., the function in the moment can be any measurable function. These problems have recently attracted growing…
We show first that there are intrinsic relationships among different conditions, old and recent, which lead to some general statements in both the Stieltjes and the Hamburger moment problems. Then we describe checkable conditions and prove…
The trigonometric moment problem arises from the study of one-parameter families of centers in polynomial vector fields. It asks for the classification of the trigonometric polynomials $Q$ which are orthogonal to all powers of a…
The aim of this paper is to provide some new criteria for the Stieltjes moment problem. We first give a Tauberian type criterion for moment indeterminacy that is expressed purely in terms of the asymptotic behavior of the moment sequence…
The power moments of a positive measure on the real line or the circle are characterized by the non-negativity of an infinite matrix, Hankel, respectively Toeplitz, attached to the data. Except some fortunate configurations, in higher…
We present a family of explicit formulae for evaluating absolute moments of probability measures on $\mathbb{R}^d$ in terms of Fourier transforms. As to the space of probability measures possessing finite absolute moments of an arbitrary…
We find conditions which guarantee moment (in)determinacy of powers and products of nonnegative random variables. We establish new and general results which are based either on the rate of growth of the moments of a random variable or on…
We review and develop the classical theory of moments of configurations of weighted points with a focus on systems with an identically vanishing first moment. The latter condition produces equations for equilibrium configurations of systems…
We consider the set M_n of all n-truncated power moment sequences of probability measures on [0,1]. We endow this set with the uniform probability. Picking randomly a point in M_n, we show that the upper canonical measure associated with…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…