相关论文: Stochastic Wiener Filter in the White Noise Space

In this article, we have analyzed semi-discrete finite element approximations of the Stochastic linear Schr\"{o}dinger equation in a bounded convex polygonal domain driven by additive Wiener noise. We use the finite element method for…

In White Noise Analysis (WNA), various random quantities are analyzed as elements of $(S)^{\ast}$, the space of Hida distributions ([1]). Hida distributions are generalized functions of white noise, which is to be naturally viewed as the…

Quantitative evaluations of differences and/or similarities between data samples define and shape optimisation problems associated with learning data distributions. Current methods to compare data often suffer from limitations in capturing…

Motivated by the traditional Lotka-Volterra competitive models, this paper proposes and analyzes a class of stochastic reaction-diffusion partial differential equations. In contrast to the models in the literature, the new formulation…

This article considers the application of particle filtering to continuous-discrete optimal filtering problems, where the system model is a stochastic differential equation, and noisy measurements of the system are obtained at discrete…

Normalizing flows transform a simple base distribution into a complex target distribution and have proved to be powerful models for data generation and density estimation. In this work, we propose a novel type of normalizing flow driven by…

Cellular signaling involves the transmission of environmental information through cascades of stochastic biochemical reactions, inevitably introducing noise that compromises signal fidelity. Each stage of the cascade often takes the form of…

Researchers from different areas have independently defined extensions of the usual weak convergence of laws of stochastic processes with the goal of adequately accounting for the flow of information. Natural approaches are convergence of…

We present two linear relations between an arbitrary (real tempered second order) generalized stochastic process over $\mathbb{R}^{d}$ and White Noise processes over $\mathbb{R}^{d}$. The first is that any generalized stochastic process can…

In this paper we study a large class of nonlinear stochastic wave equations that arise in laser generation models and models for propagation in random media in a unified mathematical framework. Continuous and pulse-wave propagation models,…

By introducing the small noise expansion techniques, we show that the fully nonlinear (non-Markovian) stochastic inflationary system, may be re-cast in terms of an infinite set of Wiener processes (stochastic equations with white noises).…

This paper provides an existence-and-uniqueness theorem characterizing the stochastic integral with respect to a Wiener process. The integral is represented as a mapping from the space of measurable and adapted pathwise locally integrable…

Motivated by the simulation of stable random fields, we consider the issue of discrete approximations of independently scattered stable noise. Two approaches are proposed: grid approximations available when the underlying space is $\bbR^d$…

A brief presentation of the basic concepts in quantum probability theory is given in comparison to the classical one. The notion of quantum white noise, its explicit representation in Fock space, and necessary results of noncommutative…

CoVariance Neural Networks (VNNs) perform graph convolutions on the empirical covariance matrix of signals defined over finite-dimensional Hilbert spaces, motivated by robustness and transferability properties. Yet, little is known about…

We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…

In this article we construct a large class of interacting Euclidean quantum field theories, over a p-adic space time, by using white noise calculus. We introduce p-adic versions of the Kondratiev and Hida spaces in order to use the Wick…

This paper studies a small-gain theorem for nonlinear stochastic equations driven by additive white noise in both trajectories and stationary distribution. Motivated by the most recent work of Marcondes de Freitas and Sontag \cite{FS3}, we…

A study on the notion of covariant derivatives in flat and curved space-time via It\^o-Wiener processes, when subjected to stochastic processes, is presented. Going into details, there is an analysis of the following topics: (i) Besov…

The problem of analyzing the Ito stochastic differential system and its filtering has received attention. The classical approach to accomplish filtering for the Ito SDE is the Kushner equation. In contrast to the classical filtering…