Related papers: Stochastic modelling of Gaussian processes by impr…

We consider the problem of estimating unknown parameters in stochastic differential equations driven by colored noise, which we model as a sequence of Gaussian stationary processes with decreasing correlation time. We aim to infer…

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,…

A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the…

We study a well-known estimator of the fractal index of a stochastic process. Our framework is very general and encompasses many models of interest; we show how to extend the theory of the estimator to a large class of non-Gaussian…

Maximum likelihood estimators for time-dependent mean functions within Gaussian processes are provided in the context of continuous observations. We find the widest possible class of mean functions for which the likelihood function can be…

We consider a measurable stationary Gaussian stochastic process. A criterion for testing hypotheses about the covariance function of such a process using estimates for its norm in the space $L_p(\mathbb {T}),\,p\geq1$, is constructed.

Additive or multiplicative stationary noise recently became an important issue in applied fields such as microscopy or satellite imaging. Relatively few works address the design of dedicated denoising methods compared to the usual white…

We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

It was shown in Mishura et al. (Stochastic Process. Appl. 123 (2013) 2353-2369), that any random variable can be represented as improper pathwise integral with respect to fractional Brownian motion. In this paper, we extend this result to…

This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary gaussian noise having unknown correlation function. A general model selection procedure on the basis of…

We discuss general multi-dimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety…

We present an exact functional formalism to deal with linear Langevin equations with arbitrary memory kernels and driven by any noise structure characterized through its characteristic functional. No others hypothesis are assumed over the…

It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it…

We consider the effect of replacing in stochastic differential equations leading to the dynamical collapse of the statevector, white noise stochastic processes with non white ones. We prove that such a modification can be consistently…

With the use of Hida's white noise space theory space theory and spaces of stochastic distributions, we present a detailed analytic continuation theory for classes of Gaussian processes, with focus here on Brownian motion. For the latter,…

This paper addresses the detection of a stochastic process in noise from irregular samples. We consider two hypotheses. The \emph{noise only} hypothesis amounts to model the observations as a sample of a i.i.d. Gaussian random variables…

Spatial process models popular in geostatistics often represent the observed data as the sum of a smooth underlying process and white noise. The variation in the white noise is attributed to measurement error, or micro-scale variability,…

A lot is known about the H\"older regularity of stochastic processes, in particular in the case of Gaussian processes. Recently, a finer analysis of the local regularity of functions, termed 2-microlocal analysis, has been introduced in a…

We perturb with an additive Gaussian white noise the Hamiltonian system associated to a cubic anharmonic oscillator. The stochastic system is assumed to start from initial conditions that guarantee the existence of a periodic solution for…