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Volume 5, Issue 6, 1 December 2021, Pages 865-880
Abstract. We develop a variational inequality approach for the inverse problem of identifying a stochastic parameter in a stochastic partial differential equation. An iteratively regularized projected stochastic gradient scheme for variational inequalities posed in a Hilbert space is proposed. By employing the martingale theory, we give a complete convergence analysis for the iterative scheme under weaker conditions on the random noise than those commonly imposed in the available literature. Preliminary numerical results on the inverse problem demonstrate the efficacy of the developed framework.
How to Cite this Article:
Baasansuren Jadamba, Akhtar A. Khan, Miguel Sama, Yidan Yang, An iteratively regularized stochastic gradient method for estimating a random parameter in a stochastic PDE. A variational inequality approach, J. Nonlinear Var. Anal. 5 (2021), 865-880.