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arXiv · 2308.15741

Stability and regularization for ill-posed Cauchy problem of a stochastic parabolic differential equation

Fangfang Dou·Peimin Lü·Yu Wang
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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.

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Fangfang Dou, Peimin Lü, Yu Wang. 2023-08-30. Stability and regularization for ill-posed Cauchy problem of a stochastic parabolic differential equation. https://arxiv.org/abs/2308.15741

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