Asymptotic Behaviors for Random Geometric Series

Fuqing Gao (), Yunshi Gao () and Xianjie Xia ()
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Fuqing Gao: Wuhan University
Yunshi Gao: Wuhan University
Xianjie Xia: Wuhan University

Journal of Theoretical Probability, 2024, vol. 37, issue 3, 2818-2842

Abstract: Abstract In this paper, we consider asymptotic behaviors for random geometric series. We first study the convergence rates in the central limit theorem, i.e., the Berry–Esseen bound and Edgeworth expansions, and precise deviations. Then we define a bounded linear operator from the path space of random walk to the path space of the random geometric series and establish the functional central limit theorem, the functional law of iterated logarithm, and functional large deviation principles for the random geometric series.

Keywords: Random geometric series; Berry–Esseen bound; Precise deviation; Functional limit theorem; Primary 60F05; 60F17; Secondary 30B20; 60F10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01327-3

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