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This review article focuses on regularised estimation procedures applicable to geostatistical and spatial econometric models. These methods are particularly relevant in the case of big geospatial data for dimensionality reduction or model…

We compare the rate of convergence to the time average of a function over an integrable Hamiltonian flow with the one obtained by a stochastic perturbation of the same flow. Precisely, we provide detailed estimates in different Fourier…

Via a unified geometric approach, a class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they are univalent. Some consequences are deduced concerning radius of convergence…

The Mat\'ern covariance function is a popular choice for modeling dependence in spatial environmental data. Standard Mat\'ern covariance models are, however, often computationally infeasible for large data sets. In this work, recent results…

We consider finite dimensional rough differential equations driven by centered Gaussian processes. Combining Malliavin calculus, rough paths techniques and interpolation inequalities, we establish upper bounds on the density of the…

In this paper, we extend Walsh's stochastic integral with respect to a Gaussian noise, white in time and with some homogeneous spatial correlation, in order to be able to integrate some random measure-valued processes. This extension turns…

We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the…

We find a representation of the integral of a Gauss-Markov process in the interval [0, t], in terms of Brownian motion. Moreover, some connections with first-passagetime problems are discussed, and some examples are reported.

We analyze Gaussian analytic functions (GAFs) defined as power series with coefficients modeled by discrete stationary Gaussian processes, utilizing their spectral measures. We revisit some limit theorems for random analytic functions and…

This paper is an overview of the classical level crossing problem which is studied extensively in the literature and is fundamental in many branches of applied probability. We discuss a number of approximations with an emphasis on their…

In this note we explore the relationship between the operation of convolution of functions and the Eulerian integrals. This approach allow us to obtain some expressions for the convolution of a certain class of functions in terms of the…

Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the…

Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…

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…

The stochastic partial differential equation analyzed in this work is the Cahn-Hilliard equation perturbed by an additive fractional white noise (fractional in time and white in space). We work in the case of one spatial dimension and apply…

The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…

A new set of symmetric correction functions is presented for high-order flux reconstruction, that expands upon, while incorporating, all previous correction function sets and opens the possibility for improved performance. By considering FR…

We address the counting of level crossings for inertial stochastic processes. We review Rice's approach to the problem and generalize the classical Rice formula to include all Gaussian processes in their most general form. We apply the…

We study the spectral properties of a stochastic process obtained by multiplicative inversion of a non-zero-mean Gaussian process. We show that its autocorrelation and power spectrum exist for most regular processes, and we find a…

We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…