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Regularization of the backward stochastic heat conduction problem
Regularization of the backward stochastic heat conduction problem
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Date
2021
Authors
Nguyen Huy Tuan
Daniel Lesnic
Tran Ngoc Thach
Tran Bao Ngoc
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Research Projects
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Abstract
In this paper, we study the backward problem for the stochastic parabolic heat equation driven by a Wiener process. We show that the problem is ill-posed by violating the continuous dependence on the input data. In order to restore stability, we apply a filter regularization method which is completely new in the stochastic setting. Convergence rates are established under different a priori assumptions on the sought solution.
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Keywords
Stochastic parabolic equations,
backward problems,
regularization,
error estimates