Consistency of the Tikhonov’s regularization in an ill-posed problem with α-mixing random data

Nabila Aiane and Abdelnasser Dahmani

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 11, 5633-5642

Abstract: In this article, we establish exponential inequalities for the probability of the distance between the approximated solution and the exact one for an operator equation with an exact right-hand side. In addition, the second member of the operator equation is observed with α-mixing random errors. These inequalities yield the almost complete convergence of the approximate solution.

Date: 2017
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DOI: 10.1080/03610926.2015.1107586

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