Related papers: White Noise Representation of Gaussian Random Fiel…
This appendix provides a short proof for sample path continuity of the Brownian motion induced by an arbitrary centered Gaussian measure on a separable Banach space, and also some perturbation results for the spectrum of compact…
In this work we review the application of the theory of Gaussian processes to the modeling of noise in pulsar-timing data analysis, and we derive various useful and optimized representations for the likelihood expressions that are needed in…
The ability of Gaussian noise to induce ordered states in dynamical systems is here presented in an overview of the main stochastic mechanisms able to generate spatial patterns. These mechanisms involve: (i) a deterministic local dynamics…
For the problem of nonparametric detection of signal in Gaussian white noise we point out strong asymptotically minimax tests. The sets of alternatives are a ball in Besov space $B^r_{2\infty}$ with "small" balls in $L_2$ removed.
In this article, we give a new proof of the It\^o formula for some integral processes related to the space-time L\'evy white noise introduced in Balan (2015) as an alternative for the Gaussian white noise perturbing an SPDE. We discuss two…
The first part of this thesis proposes a general approach to infinite dimensional non-Gaussian analysis, including the Poissonian case. In particular distribution theory is developed. Using appropriate integral transformations, generalized…
We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new…
Hadwiger integrals employ the intrinsic volumes as measures for integration of real-valued functions. We provide a formula for the expected values of Hadwiger integrals of Gaussian-related random fields. The expected Hadwiger integrals of…
We review and present some known results for non-linear functionals of Gaussian variables in the context of discrete Gaussian fields defined on the $d$ dimensional lattice. Our main result is a Central Limit Theorem in the spirit of the…
In present paper we prove an existence and give a moments estimate for the local time of Gaussian integrators. Every Gaussian integrator is associated with a continuous linear operator in the space of square integrable functions via white…
Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables…
We introduce a signal processing model for signals in non-white noise, where the exact noise spectrum is a priori unknown. The model is based on a Student's t distribution and constitutes a natural generalization of the widely used normal…
Variational Gaussian process (GP) approximations have become a standard tool in fast GP inference. This technique requires a user to select variational features to increase efficiency. So far the common choices in the literature are…
The problem of detecting a wide-sense stationary Gaussian signal process embedded in white Gaussian noise, where the power spectral density of the signal process exhibits uncertainty, is investigated. The performance of minimax robust…
The concepts of Feynman integrals in white noise analysis are used to realize the Feynman integrand for a charged particle in a constant magnetic field as a Hida distribution. For this purpose we identify the velocity dependent potential as…
We present the continuous wavelet transform (WT) of white Gaussian noise and establish a connection to the theory of Gaussian analytic functions. Based on this connection, we propose a methodology that detects components of a signal in…
Some integration techniques for real-valued functions with respect to vector measures with values in Banach spaces (and viceversa) are investigated in order to establish abstract versions of classical theorems of Probability and Stochastic…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
In this article, we will construct an approximation of Gaussian white noise based on the sequence of Bernoulli random variables and define Wick's products and the stochastic exponent for the Bernoulli case. Here we will propose a method to…
Signal processing in non-Gaussian noise environment is addressed in this paper. For many real-life situations, the additive noise process present in the system is found to be dominantly non-Gaussian. The problem of detection and estimation…