Related papers: Averaging Gaussian functionals
We study asymptotic expansions of Gaussian integrals of analytic functionals on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an asymptotic equality coupling the Gaussian integral and the trace of the composition of…
In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise…
We introduce a spatial averaging scheme and use it to study the evolution of spatial averages in large-scale simulations of cosmological structure formation performed with the Einstein Toolkit. The averages are performed on the spatial…
Fractional Gaussian noise models the time series with long-range dependence; when the Hurst index $H>1/2$, it has positive correlation reflecting a persistent autocorrelation structure. This paper studies the numerical method for solving…
Semiclassical Physics in gravitational scenario, in its first approximation (1st order) cares only for the expectation value of stress energy tensor and ignores the inherent quantum fluctuations thereof. In the approach of stochastic…
We develop a statistical framework for conducting inference on collections of time-varying covariance operators (covariance flows) over a general, possibly infinite dimensional, Hilbert space. We model the intrinsically non-linear structure…
The fluctuations of the work done by an external Gaussian random force on a harmonic oscillator that is also in contact with a thermal bath is studied. We have obtained the exact large deviation function as well as the complete asymptotic…
We study $d$-variate problem in the average case setting with respect to a zero-mean Gaussian measure. The covariance kernel of this Gaussian measure is a product of univariate kernels and satisfies some special properties. We study $(s,…
All prior applications of Diffusing-Wave Spectroscopy (DWS) to aqueous foams rely upon the assumption that the electric field of the detected light is a Gaussian random variable and that, hence, the Siegert relation applies. Here we test…
Motivated by the analysis of spectrometric data, we introduce a Gaussian graphical model for learning the dependence structure among frequency bands of the infrared absorbance spectrum. The spectra are modeled as continuous functional data…
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…
For a spatiotemporal process $\{X_j(s,t) | ~s \in S~,~t \in T \}_{j =1, \ldots , n} $, where $S$ denotes the set of spatial locations and $T$ the time domain, we consider the problem of testing for a change in the sequence of mean…
We study the time-dependent spatial averages of a critical stochastic partial differential equation, namely the stochastic heat equation in dimension $d\geq 3$ with noise white in time and colored in space with covariance kernel…
This work introduces the Gaussian integration to address a smoothing problem of a nonlinear stochastic state space model. The probability densities of states at each time instant are assumed to be Gaussian, and their means and covariances…
Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein- Langevin…
Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and…
A spatial curve dynamical model framework is adopted for functional prediction of counts in a spatiotemporal log-Gaussian Cox process model. Our spatial functional estimation approach handles both wavelet-based heterogeneity analysis in…
The wave speed of a stochastic wave equation driven by Riesz noise on the unbounded multidimensional spatial domain is estimated based on discrete measurements. Central limit theorems for second-order variations of the observations in…
We consider the hydrodynamic limit in the macroscopic regime of the coupled system of stochastic differential equations, $ d\lambda_t^i=\frac{1}{\sqrt{N}} dW_t^i - V'(\lambda_t^i) dt+ \frac{\beta}{2N} \sum_{j\not=i}…
We consider the stochastic heat equation on $\mathbb R^d$ with multiplicative space-time white noise noise smoothed in space. For $d\geq 3$ and small noise intensity, the solution is known to converge to a strictly positive random variable…