Related papers: Uniform Continuity in Distribution for Borel Trans…

We study perturbations of random dynamical systems whose associated transfer operators admit a uniform spectral gap. We provide a $k^{\text{th}}$-order approximation for the invariant density of the associated random dynamical system. We…

New results on uniform convergence in probability for the most general classes of wavelet expansions of stationary Gaussian random processes are given.

We find sufficient conditions for the existence of an exact uniform modulus continuity for the class of $q$-isotropic Gaussian random fields introduced in [8]. We apply the result to a $d$-dimensional version of the $B^{\gamma}$ Gaussian…

In this note, we show that the limiting spectral distribution of symmetric random matrices with stationary entries is absolutely continuous under some sufficient conditions. This result is applied to obtain sufficient conditions on a…

There is only one fully supported ergodic invariant probability measure for the adic transformation on the space of infinite paths in the graph that underlies the Eulerian numbers. This result may partially justify a frequent assumption…

The present paper proposes a new condition to replace both the ($O$-regularly varying) quasimonotone condition and a certain type of bounded variation condition, and shows the same conclusion for the uniform convergence of certain…

The Borel summability in the distributional sense is established of the divergent perturbation theory for the ground state resonance of the quantum H\'enon-Heiles model.

This paper studies transition probabilities from a Borel subset of a Polish space to a product of two Borel subsets of Polish spaces. For such transition probabilities it introduces and studies the property of semi-uniform Feller…

In this article, we characterize both Lusin's theorem and the existence of Borel representatives via the regularity properties of the measure in general topological measure spaces. As a corollary, we prove that Borel regularity of the…

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…

We systematically find conditions which yield locally uniform convergence in the Fourier inversion formula in one and higher dimensions. We apply the gained knowledge to the complex inversion formula of the Laplace transform to extend known…

We examine the uniform distribution theory of H. Weyl when there is a periodic perturbation present. As opposed to the classical setting, in this case the conditions for (mod 1) density and (mod 1) uniform distribution turn out to be…

We establish general conditions under which there exists uniform in time convergence between a stochastic process and its approximated system. These standardised conditions consist of a local in time estimate between the original and the…

This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusions. We obtain necessary and sufficient conditions for the exponential convergence to a unique quasi-stationary distribution in total variation,…

We give a complete list of the Lebesgue-Jordan decomposition of Boolean and monotone stable distributions and a complete list of the mode of them. They are not always unimodal.

We prove that an equivalent condition for a uniform space to be coverable is that the images of the natural projections in the fundamental inverse system are uniformly open in a certain sense. As corollaries we (1) obtain a concrete way to…

In a paper entitled singularities of invariant densities for random switching between two linear odes in 2D, Bakhtin et al [5], consider a Markov process obtained by random switching between two stable linear vector fields in the plane and…

We derive necessary conditions for localization of continuous frames in terms of generalized Beurling densities. As an important application we provide necessary density conditions for sampling and interpolation in a very large class of…

Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed…

We consider how some methods of uniform and nonuniform interpolation by translates of radial basis functions -- specifically the so-called general multiquadrics -- perform in the presence of certain types of noise. These techniques provide…