Functional Large Deviation Principle and Functional Laws of Iterated Logarithm for Random Dirichlet Series

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

Journal of Theoretical Probability, 2026, vol. 39, issue 1, 1-30

Abstract: Abstract We first transfer functional limit problems in random Dirichlet series to the corresponding problems in the weighted random walk via the Laplace transform and establish some functional limit theorems for the weighted random walk. Then, we derive the large deviation principle in the path space and the functional law of iterated logarithm for the random Dirichlet series.

Keywords: Random Dirichlet series; Laplace transform; Functional large deviation principle; Functional law of iterated logarithm; Weighted random walk; 60F17; 60F10; 60G17; 60G50 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10959-025-01461-6

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