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We propose a definition of directional multivariate subexponential and convolution equivalent densities and find a useful characterization of these notions for a class of integrable and almost radial decreasing functions. We apply this…

Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but…

We introduce the notion of perturbations of quantum stochastic models using the series product, and establish the asymptotic convergence of sequences of quantum stochastic models under the assumption that they are related via a right series…

We observe $n$ inhomogeneous Poisson processes with covariates and aim at estimating their intensities. We assume that the intensity of each Poisson process is of the form $s (\cdot, x)$ where $x$ is the covariate and where $s$ is an…

This paper investigates a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from returns and expert opinions in the form of noisy signals about the current…

We construct a white noise theory and white noise calculus for the (multi-parameter) L\' evy sheet and its compensated Poisson random measures. The theory applies to stochastic partial differential equations subject to L\' evy noise.

Nonparametric regression problems with qualitative constraints such as monotonicity or convexity are ubiquitous in applications. For example, in predicting the yield of a factory in terms of the number of labor hours, the monotonicity of…

We propose a method for variable selection in the intensity function of spatial point processes that combines sparsity-promoting estimation with noise-robust model selection. As high-resolution spatial data becomes increasingly available…

In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…

Most existing image denoising approaches assumed the noise to be homogeneous white Gaussian distributed with known intensity. However, in real noisy images, the noise models are usually unknown beforehand and can be much more complex. This…

This letter establishes the asymptotic optimality of equal power allocation for measurements of a continuous wide-sense stationary (WSS) random process with a square-integrable autocorrelation function when linear estimation is used on…

Frequentist-style large-sample properties of Bayesian posterior distributions, such as consistency and convergence rates, are important considerations in nonparametric problems. In this paper we give an analysis of Bayesian asymptotics…

This paper considers the problem of adaptive estimation of a non-homogeneous intensity function from the observation of n independent Poisson processes having a common intensity that is randomly shifted for each observed trajectory. We show…

Sparse linear inverse problems appear in a variety of settings, but often the noise contaminating observations cannot accurately be described as bounded by or arising from a Gaussian distribution. Poisson observations in particular are a…

We study a model of a nonlinear oscillator with a random frequency and derive the asymptotic behavior of the probability distribution function when the noise is white. In the small damping limit, we show that the physical observables grow…

The sample paths of white noise are proved to be elements of certain Besov spaces with dominating mixed smoothness. Unlike in isotropic spaces, here the regularity does not get worse with increasing space dimension. Consequently, white…

We investigate and compare the fundamental performance of several distributed learning methods that have been proposed recently. We do this in the context of a distributed version of the classical signal-in-Gaussian-white-noise model, which…

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 first exhibit a multimodal image registration task, for which a neural network trained on a dataset with noisy labels reaches almost perfect accuracy, far beyond noise variance. This surprising auto-denoising phenomenon can be explained…

Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…