Related papers: Spatial and Temporal white noises under sublinear …
Incredible progress on the theoretical uncertainty of the spatial correlations of the stochastic gravitational wave (GW) background were recently made. However, it remains to realize the impact of this theoretical uncertainty on PTA cross…
Power-law noises abound in nature and have been observed extensively in both time series and spatially varying environmental parameters. Although, recent years have seen the extension of traditional stochastic partial differential equations…
Using tools from the theory of random fields with stationary increments, we introduce a new class of processes which can be used as a model for the noise perturbing an SPDE. This type of noise (called harmonizable) is not necessarily…
We consider the problem of parameter estimation by the observations of deterministic signal in white gaussian noise. It is supposed that the signal has a singularity of cusp-type. The properties of the maximum likelihood and bayesian…
This paper is concerned with the estimation of the period of an unknown periodic function in Gaussian white noise. A class of estimators of the period is constructed by means of a penalized maximum likelihood method. A second-order…
We construct a time-consistent sublinear expectation in the setting of volatility uncertainty. This mapping extends Peng's G-expectation by allowing the range of the volatility uncertainty to be stochastic. Our construction is purely…
We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for forecasting time series of spatial processes, i.e. series of observations sharing temporal and spatial dependencies. The model learns these…
We give a theory of sublinear expectations and martingales in discrete time. Without assuming the existence of a dominating probability measure, we derive the extensions of classical results on uniform integrability, optional stopping of…
We present simple classical dynamical models to address the question of introducing a stochastic nature in a time variable. These models include noise in the time variable but not in the "space" variable, which is opposite to the normal…
We study strictly parabolic stochastic partial differential equations on $\R^d$, $d\ge 1$, driven by a Gaussian noise white in time and coloured in space. Assuming that the coefficients of the differential operator are random, we give…
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,…
We introduce the notions of sub Gaussian random variables in sub-linear expectation spaces. To avoid the problem caused by the existence of two different expectations, i.e., the upper expectation and the lower expectation, we divide the…
In this paper, we establish the existence and uniqueness of invariant measures for a class of semilinear stochastic partial differential equations driven by multiplicative noise on a bounded domain. The main results can be applied to SPDEs…
Classical Gaussian white noise in communications and signal processing is viewed as the limit of zero mean second order Gaussian processes with a compactly supported flat spectral density as the support goes to infinity. The difficulty of…
This paper investigate the local times and modulus of nondifferentiability of the spherical Gaussian random fields. We extend the methods for studying the local times of Gaussian to the spherical setting. The new main ingredient is the…
Geographical and Temporal Weighted Regression (GTWR) model is an important local technique for exploring spatial heterogeneity in data relationships, as well as temporal dependence due to its high fitting capacity when it comes to real…
In a recent work [DDRZ20], it has been developed a novel framework aimed at studying at a perturbative level a large class of non-linear, scalar, real, stochastic PDEs and inspired by the algebraic approach to quantum field theory. The main…
A harmonic oscillator under influence of the noise is a basic model of various physical phenomena. Under Gaussian white noise the position and velocity of the oscillator are independent random variables which are distributed according to…
This paper investigates the problem of adjusting for spatial effects in genomic prediction. Despite being seldomly considered in genomic prediction, spatial effects often affect phenotypic measurements of plants. We consider a Gaussian…
We consider a nonlinear stochastic partial differential equation (SPDE) in divergence form where the forcing term is a Gaussian noise, that is white in time and colored in space such that the gradient of the solution is H\"older-continuous,…