Related papers: A moment problem for pseudo-positive definite func…
In this work we present two particular cases of the general duality result for linear optimisation problems over signed measures with infinitely many constraints in the form of integrals of functions with respect to the decision variables…
We show that the pointlike and the idempotent pointlike problems are reducible with respect to natural signatures in the following cases: the pseudovariety of all finite semigroups in which the order of every subgroup is a product of…
We consider sensitivity of a semidefinite program under perturbations in the case that the primal problem is strictly feasible and the dual problem is weakly feasible. When the coefficient matrices are perturbed, the optimal values can…
We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…
The Moment-SOS hierarchy initially introduced in optimization in 2000, is based on the theory of the K-moment problem and its dual counterpart, polynomials that are positive on K. It turns out that this methodology can be also applied to…
We solve the truncated K-moment problem when $K\subseteq R^n$ is the closure of a, not necessarily bounded, open set (which includes the important cases $K=R^n$ and $K=R^n_+$). That is, we completely characterize the interior of the convex…
A moment body is a linear projection of the spectraplex, the convex set of trace-one positive semidefinite matrices. Determining whether a given point lies within a given moment body is a problem with numerous applications in quantum state…
Suppose we are given two probability measures on the set of one-way infinite finite-alphabet sequences and consider the question when one of the measures predicts the other, that is, when conditional probabilities converge (in a certain…
We prove the open question posed by Zhuang and Hu in Remark 3.1. More generally, we consider symmetric joint probability mass functions and joint densities whose associated quadratic form is non-negative. In this class, for every \(r>0\),…
In this paper we give refinements of some convex and log-convex moment inequalities of the first and second order using a special kind of positive semi-definite form. An open problem concerning eight parameter refinement of second order is…
In this work we investigate and characterize linear functionals $L:\mathbb{R}[x_1,\dots,x_n]\to\mathbb{R}$ with absolutely continuous representing measures $\mu$, i.e., $\mathrm{d}\mu(x) = g(x)\,\mathrm{d} x$ for some density $g$. We focus…
We study time-consistency questions for processes of monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of…
Necessary and sufficient conditions for weak and vague convergence of measures are important for a diverse host of applications. This paper aims to give a comprehensive description of the relationship between the two modes of convergence…
For a general class of diffusion processes with multiplicative noise, describing a variety of physical as well as financial phenomena, mostly typical of complex systems, we obtain the analytical solution for the moments at all times. We…
One solution to the so-called problem of time is to construct certain Dirac observables, sometimes called evolving constants of motion. There has been some discussion in the literature about the interpretation of such observables, and in…
The sequence of moments of a vector-valued random variable can characterize its law. We study the analogous problem for path-valued random variables, that is stochastic processes, by using so-called robust signature moments. This allows us…
In the recent paper arXiv:0710.4085 was shown that any solution of "the polynomial moment problem", which asks to describe polynomials Q orthogonal to all powers of a given polynomial P on a segment, may be obtained as a sum of some…
We obtain for the Kempner series (i.e. harmonic series where certain digits are excluded from all denominators, for example the digit 9 in base 10) new representations as geometrically convergent series. The coefficients for these…
The multivariate moment problem is investigated in the general context of the polynomial algebra $\mathbb{R}[x_i \mid i \in \Omega]$ in an arbitrary number of variables $x_i$, $i\in \Omega$. The results obtained are sharpest when the index…
We provide a geometric characterization of the closed sets $K \subseteq \mathbb{R}^d$ such that every real $d$-sequence is the moment sequence of some Schwartz function on $\mathbb{R}^d$ with support in $K$. We obtain a similar result for…