Determination the Solution of a Stochastic Parabolic Equation by the Terminal Value
Numerical Analysis
2022-06-29 v1 Numerical Analysis
Abstract
This paper studies the inverse problem of determination the history for a stochastic diffusion process, by means of the value at the final time . By establishing a new Carleman estimate, the conditional stability of the problem is proven. Based on the idea of Tikhonov method, a regularized solution is proposed. The analysis of the existence and uniqueness of the regularized solution, and proof for error estimate under an a-proior assumption are present. Numerical verification of the regularization, including numerical algorithm and examples are also illustrated.
Keywords
Cite
@article{arxiv.2202.05439,
title = {Determination the Solution of a Stochastic Parabolic Equation by the Terminal Value},
author = {Fangfang Dou and Wanli Du},
journal= {arXiv preprint arXiv:2202.05439},
year = {2022}
}