Lindeberg’s Method for Moderate Deviations and Random Summation

Peter Eichelsbacher () and Matthias Löwe ()
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Peter Eichelsbacher: Ruhr-Universität Bochum
Matthias Löwe: Westfälische Wilhelms-Universität Münster, Fachbereich Mathematik

Journal of Theoretical Probability, 2019, vol. 32, issue 2, 872-897

Abstract: Abstract We apply Lindeberg’s method, invented to prove a central limit theorem, to analyze the moderate deviations around such a central limit theorem. In particular, we will show moderate deviation principles for martingales as well as for random sums, in the latter situation in both the cases when the limit distribution is Gaussian or non-Gaussian. Moreover, in the Gaussian case we show moderate deviations for random sums using bounds on cumulants, alternatively. Finally, we also prove a large deviation principle for certain random sums.

Keywords: Random sums; Moderate and large deviations; Lindeberg’s method; 60F05; 60F10; 60G50 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-019-00881-5

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