相关论文: Regularity of Gaussian Processes on Dirichlet spac…

We prove two compactness results for function spaces with finite Dirichlet energy of half-space nonlocal gradients. In each of these results, we provide sufficient conditions on a sequence of kernel functions that guarantee the asymptotic…

An analogue of the classical Mecke formula for Poisson point processes is proved for the class of space-time STIT tessellation processes. From this key identity the Markov property of a class of associated random processes is derived. This…

We show that one can characterize the Besov spaces on a smooth compact oriented Riemannian manifold, for the full range of indices, through a knowledge of the size of frame coefficients, using the frames we have constructed in [8].

Current methods for regularization in machine learning require quite specific model assumptions (e.g. a kernel shape) that are not derived from prior knowledge about the application, but must be imposed merely to make the method work. We…

Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…

Let $1 \leq d < D$ and $(p,q,s)$ satisfying $0 < p < \infty$, $0 < q \leq \infty$, $0 < s-d/p < \infty$. In this article we study the global and local regularity properties of traces, on affine subsets of $\R^D$, of functions belonging to…

A method to perform unfolding with Gaussian processes (GPs) is presented. Using Bayesian regression, we define an estimator for the underlying truth distribution as the mode of the posterior. We show that in the case where the bin contents…

Starting with a transient irreducible diffusion process $X^0$ on a locally compact separable metric space $(D, d)$, one can construct a canonical symmetric reflected diffusion process $\bar X$ on a completion $D^*$ of $(D, d)$ through the…

Gaussian processes are a flexible Bayesian nonparametric modelling approach that has been widely applied but poses computational challenges. To address the poor scaling of exact inference methods, approximation methods based on sparse…

We establish that the Dirichlet problem for convex linear growth functionals on $BD$, the functions of bounded deformation, gives rise to the same unconditional Sobolev and partial $C^{1,\alpha}$-regularity theory as presently available for…

In this paper, we derive explicit sharp two-sided estimates for the Dirichlet heat kernels of a large class of symmetric (but not necessarily rotationally symmetric) L\'evy processes on half spaces for all $t>0$. These L\'evy processes may…

In the paper we prove the existence of probabilistic solutions to systems of the form $-Au=F(x,u)+\mu$, where $F$ satisfies a generalized sign condition and $\mu$ is a smooth measure. As for $A$ we assume that it is a generator of a Markov…

This paper gives some relating results for various concepts of convexity in metric spaces such as midpoint convexity, convex structure, uniform convexity and near-uniform convexity, Busemann curvature and its relation to convexity. Some…

In this paper, quantitative bounds in high-frequency central limit theorems are derived for Poisson based $U$-statistics of arbitrary degree built by means of wavelet coefficients over compact Riemannian manifolds. The wavelets considered…

We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces $Z$. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices $s<1,$ as well as the first order…

We study the convergence of centered and normalized sums of i.i.d. random elements of the space $\mathcal{D}$ of c{{\'a}}dl{{\'a}}g functions endowed with Skorohod's $J\_1$ topology, to stable distributions in $\mathcal D$. Our results are…

We begin with isotropic Gaussian random fields, and show how the Bochner-Godement theorem gives a natural way to describe their covariance structure. We continue with a study of Mat\'ern processes on Euclidean space, spheres, manifolds and…

We study mean value properties of harmonic functions in metric measure spaces. The metric measure spaces we consider have a doubling measure and support a (1,1)- Poincar\'e inequality. The notion of harmonicity is based on the Dirichlet…

We propose an algorithm to approximate solutions of global optimization problems in Sobolev spaces that follows the spirit of Consensus-based algorithms in finite dimensions. The main ingredient are Gaussian processes. In fact, we exploit…

For every natural number k we prove a decomposition theorem for bounded measurable functions on compact abelian groups into a structured part, a quasi random part and a small error term. In this theorem quasi randomness is measured with the…