Related papers: On the equivalence of probability spaces

A recurrent theme in functional analysis is the interplay between the theory of positive definite functions, and their reproducing kernels, on the one hand, and Gaussian stochastic processes, on the other. This central theme is motivated by…

We introduce a new approach to the spectral equivalence of Gaussian processes and fields, based on the methods of operator theory in Hilbert space. Besides several new results including identities in law of quadratic norms for integrated…

We study a family of stationary increment Gaussian processes, indexed by time. These processes are determined by certain measures sigma (generalized spectral measures), and our focus here is on the case when the measure sigma is a singular…

Let $(\Omega,\mathcal{F})$ be a standard Borel space and $\mathcal{P}(\mathcal{F})$ the collection of all probability measures on $\mathcal{F}$. Let $E\subset\Omega\times\Omega$ be a measurable equivalence relation, that is,…

In this paper we display a family of Gaussian processes, with explicit formulas and transforms. This is presented with the use of duality tools in such a way that the corresponding path-space measures are mutually singular. We make use of a…

Quadratic variations of Gaussian processes play important role in both stochastic analysis and in applications such as estimation of model parameters, and for this reason the topic has been extensively studied in the literature. In this…

Gaussian processes (GPs) offer a principled probabilistic model over functions, but exact inference is restricted to the linear-Gaussian regime. We establish an explicit equivalence between GPs and a class of linear diffusion models,…

We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…

We consider a symmetric matrix-valued Gaussian process $Y^{(n)}=(Y^{(n)}(t);t\ge0)$ and its empirical spectral measure process $\mu^{(n)}=(\mu_{t}^{(n)};t\ge0)$. Under some mild conditions on the covariance function of $Y^{(n)}$, we find an…

In this paper we develop non-asymptotic Gaussian approximation results for the sampling distribution of suprema of empirical processes when the indexing function class $\mathcal{F}_n$ varies with the sample size $n$ and may not be Donsker.…

We consider a class of stochastic processes $X$ defined by $X\left( t\right) =\int_{0}^{T}G\left( t,s\right) dM\left( s\right) $ for $t\in\lbrack0,T]$, where $M$ is a square-integrable continuous martingale and $G$ is a deterministic…

We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian…

Given a set of moment restrictions (MRs) that overidentify a parameter $\theta$, we investigate a semiparametric Bayesian approach for inference on $\theta$ that does not restrict the data distribution $F$ apart from the MRs. As main…

We consider Gaussian measures $\mu, \tilde{\mu}$ on a separable Hilbert space, with fractional-order covariance operators $A^{-2\beta}$ resp. $\tilde{A}^{-2\tilde{\beta}}$, and derive necessary and sufficient conditions on $A, \tilde{A}$…

This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing…

We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…

This paper explores certain kinds of empirical process with respect to the components of multivariate Gaussian. We put forward some finite sample bounds which hold for multivariate Gaussian under general dependence. We give necessary and…

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

In this paper we present the groundwork for an It\^o/Malliavin stochastic calculus and Hida's white noise analysis in the context of a supersymmentry with Z3-graded algebras. To this end we establish a ternary Fock space and the…

In this article we study existence of pathwise stochastic integrals with respect to a general class of $n$-dimensional Gaussian processes and a wide class of adapted integrands. More precisely, we study integrands which are functions that…