相关论文: Vague convergence and method of moments for random…
In this paper we introduce a metrics on the space of idempotent probability measures on a given compactum, which extends the metrics on the compactum. It is proven the introduced metrics generates the pointwise convergence topology on the…
It is well established that starting only with strong, projective quantum measurements, experiments can be designed to allow weak measurements, which lead to random walk between the possible final measurement outcomes. However, one can ask…
A local convergence rate is established for a Gauss orthogonal collocation method applied to optimal control problems with control constraints. If the Hamiltonian possesses a strong convexity property, then the theory yields convergence for…
In this article we extend the notion of metric measure spaces to so-called metric two-level measure spaces (m2m spaces): An m2m space $(X, r, \nu)$ is a Polish metric space $(X, r)$ equipped with a two-level measure $\nu \in…
We establish convergence to an invariant measure as time tends to infinity, for a large class of (possibly non-Markovian) stochastic volatility models. Our arguments are based on a novel coupling idea for Markov chains which also extends to…
We refute the widely held belief that the quantum weak value necessarily pertains to weak measurements. To accomplish this, we use the transverse position of a beam as the detector for the conditioned von Neumann measurement of a system…
We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…
The aim of this paper is to study the full $K-$moment problem for measures supported on some particular non-linear subsets $K$ of an infinite dimensional vector space. We focus on the case of random measures, that is $K$ is a subset of all…
In this paper we propose a method to construct probability measures on the space of convex bodies with a given pushforward distribution. Concretely we show that there is a measure on the metric space of centrally symmetric convex bodies,…
This paper characterizes the maximum mean discrepancies (MMD) that metrize the weak convergence of probability measures for a wide class of kernels. More precisely, we prove that, on a locally compact, non-compact, Hausdorff space, the MMD…
We propose a notion of graph convergence that interpolates between the Benjamini--Schramm convergence of bounded degree graphs and the dense graph convergence developed by L\'aszl\'o Lov\'asz and his coauthors. We prove that spectra of…
While there exists a well-developed asymptotic theory of Fr\'echet means of random variables taking values in a general "finite-dimensional" metric space, there are only a few known results in which the random variables can take values in…
Aim of this paper is to discuss convergence of pointed metric measure spaces in absence of any compactness condition. We propose various definitions, show that all of them are equivalent and that for doubling spaces these are also…
Concentration of measure is a phenomenon in which a random variable that depends in a smooth way on a large number of independent random variables is essentially constant. The random variable will "concentrate" around its median or…
In this paper, we study the existence of the random approximations and fixed points for random almost lower semicontinuous operators defined on finite dimensional Banach spaces, which in addition, are condensing or 1-set-contractive. Our…
This expository note aims at illustrating weak convergence of probability measures from a broader view than a previously published paper. Though the results are standard for functional analysts, this approach is rarely known by…
Prokhorov's Theorem in probability theory states that a family $\Gamma$ of probability measures on a Polish space is tight if and only if every sequence in $\Gamma$ has a weakly convergent subsequence. Due to the highly non-constructive…
We study the weak finite element method solving convection-diffusion equations. A weak finite element scheme is presented based on a spacial variational form. We established a weak embedding inequality that is very useful in the weak finite…
Variable order structures model situations in which the comparison between two points depends on a point-to-cone map. In this paper, an inexact projected gradient method for solving smooth constrained vector optimization problems on…
We discuss a conjecture about comparability of weak and strong moments of log-concave random vectors and show the conjectured inequality for unconditional vectors in normed spaces with a bounded cotype constant.