Related papers: Oscillating Gaussian Processes

This paper is devoted to filtering, smoothing, and prediction of polynomial processes that are partially observed. These problems are known to allow for an explicit solution in the simpler case of linear Gaussian state space models. The key…

We consider the problem of frequency estimation of the periodic signal multiplied by a stationary Gaussian process (Ornstein-Uhlenbeck) and observed in the presence of the white Gaussian noise. We show the consistency and asymptotic…

we show that the solution to an oscillatory-singularly perturbed ordinary differential equation may be asymptotically expanded into a sum of oscillating terms. Each of those terms writes as an oscillating operator acting on the solution to…

We derive the asymptotic behavior for an additive functional of two independent self-similar Gaussian processes when their intersection local time exists, using the method of moments.

A quasi-static process is realized in a purely quantum-mechanical model which is described by oscillator (or particle) systems having relative-phase interactions. Time development of a mixture of two oscillator (or particle) systems which…

This paper is concerned with the problem of how to speed up computation for Gaussian process models trained on autocorrelated data. The Gaussian process model is a powerful tool commonly used in nonlinear regression applications. Standard…

This work is intended as a contribution to a wavelet-based adaptive estimator of the memory parameter in the classical semi-parametric framework for Gaussian stationary processes. In particular we introduce and develop the choice of a…

We present a new framework for recycling independent variational approximations to Gaussian processes. The main contribution is the construction of variational ensembles given a dictionary of fitted Gaussian processes without revisiting any…

This paper gives a brief introduction to some important fractional and multifractional Gaussian processes commonly used in modelling natural phenomena and man-made systems. The processes include fractional Brownian motion (both standard and…

Gaussian quadrature rules are a classical tool for the numerical approximation of integrals with smooth integrands and positive weight functions. We derive and expicitly list asymptotic expressions for the points and weights of Gaussian…

We study the asymptotic behavior of estimators of a two-valued, discontinuous diffusion coefficient in a Stochastic Differential Equation, called an Oscillating Brownian Motion. Using the relation of the latter process with the Skew…

This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…

We consider a real Gaussian process $X$ having a global unknown smoothness $(r_{\scriptscriptstyle 0},\beta_{\scriptscriptstyle 0})$, $r_{\scriptscriptstyle 0}\in \mathds{N}_0$ and $\beta_{\scriptscriptstyle 0} \in]0,1[$, with…

Gaussian states, operations, and measurements are central building blocks for continuous-variable quantum information processing which paves the way for abundant applications, especially including network-based quantum computation and…

A moderate deviation principle for nonlinear functions of Gaussian processes is established. The nonlinear functions need not be locally bounded. Especially, the logarithm is allowed. (Thus, small deviations of the process are relevant.)…

In the regime where the parameter beta is proportional to the reciprocal of the system size, it is known that the empirical distribution of Gaussian beta ensembles (resp.\ beta Laguerre ensembles) converges to a probability measure of…

Dynamical systems with $\epsilon$ small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a…

In this article, we present some specific aspects of symmetric Gamma process mixtures for use in regression models. We propose a new Gibbs sampler for simulating the posterior and we establish adaptive posterior rates of convergence related…

We algorithmically construct multi-output Gaussian process priors which satisfy linear differential equations. Our approach attempts to parametrize all solutions of the equations using Gr\"obner bases. If successful, a push forward Gaussian…

In this article we study the asymptotic behaviour of the realized quadratic variation of a process $\int_{0}^{t}u_{s}dG^{H}_{s}$, where $u$ is a $\beta$-H\"older continuous process with $\beta >1-H$ and $G^H$ is a self-similar Gaussian…