Stability and regularization for ill-posed Cauchy problem of a stochastic parabolic differential equation
Numerical Analysis
2024-05-13 v2 Numerical Analysis
Abstract
In this paper, we investigate an ill-posed Cauchy problem involving a stochastic parabolic equation. We first establish a Carleman estimate for this equation. Leveraging this estimate, we derive the conditional stability and convergence rate of the Tikhonov regularization method for the aforementioned ill-posed Cauchy problem. To complement our theoretical analysis, we employ kernel-based learning theory to implement the completed Tikhonov regularization method for several numerical examples.
Keywords
Cite
@article{arxiv.2308.15741,
title = {Stability and regularization for ill-posed Cauchy problem of a stochastic parabolic differential equation},
author = {Fangfang Dou and Peimin Lü and Yu Wang},
journal= {arXiv preprint arXiv:2308.15741},
year = {2024}
}