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Almost complete convergence for the sequence of approximate solutions in linear calibration problem with α-mixing random data

Khalfoune Samia (Laboratoire de Mathématiques Appliquées, Faculté des Sciences Exactes, Université de Bejaia, Bejaia, Algérie), khalfounesamia93@gmail.com
Zerouati Halima (Laboratoire de Mathématiques Appliquées, Faculté des Sciences Exactes, Université de Bejaia, Bejaia, Algérie), h_zerouati@yahoo.fr

In this work, we propose a stochastic method which gives an estimated solution for a linear calibration problem with α-mixing random data. We establish exponential inequalities of Fuk Nagaev type, for the probability of the distance between the approximate solutions and the exact one. Furthermore, we build a confidence domain for the so mentioned exact solution. To check the validity of our results, a numerical example is proposed.

Keywords: calibration, α-mixing random data, ill-posed problem, almost complete convergence