A stochastic procedure to solve linear ill-posed problems

Fouad Maouche, Abdelnasser Dahmani and Nadji Rahmania

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 3, 1519-1531

Abstract: In this work, we propose a stochastic procedure of Robbins–Monro type to resolve linear inverse problems in Hilbert space. We study the probability of large deviation between the exact solution and the approximated one and build a confidence domain for the approximated solution while precising the rate of convergence. To check the validity of our work, we give a simulation application into a deconvolution problem.

Date: 2017
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DOI: 10.1080/03610926.2015.1019153

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