Local linearization for estimating the diffusion parameter of nonlinear stochastic wave equations with spatially correlated noise

Fuente: arXiv
Enregistré dans:
Détails bibliographiques
Auteurs principaux: Liu, Guoping, Wang, Ran
Format: Preprint
Publié: 2025
Sujets:
Accès en ligne:
Tags: Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
_version_ 1866912622909063168
author Liu, Guoping
Wang, Ran
author_facet Liu, Guoping
Wang, Ran
contents We study the bi-parameter local linearization of the one-dimensional nonlinear stochastic wave equation driven by a Gaussian noise, which is white in time and has a spatially homogeneous covariance structure of Riesz-kernel type. We establish that the second-order increments of the solution can be approximated by those of the corresponding linearized wave equation, modulated by the diffusion coefficient. These findings extend the previous results of Huang et al. \cite{HOO2024}, which addressed the case of space-time white noise. As applications, we analyze the quadratic variation of the solution and construct a consistent estimator for the diffusion parameter.
format Preprint
id arxiv_https___arxiv_org_abs_2510_01627
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Local linearization for estimating the diffusion parameter of nonlinear stochastic wave equations with spatially correlated noise
Liu, Guoping
Wang, Ran
Probability
60H15, 60G17, 60G22
We study the bi-parameter local linearization of the one-dimensional nonlinear stochastic wave equation driven by a Gaussian noise, which is white in time and has a spatially homogeneous covariance structure of Riesz-kernel type. We establish that the second-order increments of the solution can be approximated by those of the corresponding linearized wave equation, modulated by the diffusion coefficient. These findings extend the previous results of Huang et al. \cite{HOO2024}, which addressed the case of space-time white noise. As applications, we analyze the quadratic variation of the solution and construct a consistent estimator for the diffusion parameter.
title Local linearization for estimating the diffusion parameter of nonlinear stochastic wave equations with spatially correlated noise
topic Probability
60H15, 60G17, 60G22
url https://arxiv.org/abs/2510.01627