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Precise Tail Behaviour of Some Dirichlet Series

Autor(en)
Iksanov, Alexander ; Wachtel, Vitali
Normierter Zeitschriftentitel
Journal of theoretical probability 
DOI
10.1007/s10959-024-01318-4
URL
https://pub.uni-bielefeld.de/record/2988206
Web of Science-ID
001176098400001

Weitere Details

Sprache
englisch
Darstellungsform
Text
Schlagwörter
Change of measure , Dirichlet series , Local limit theorem , Precise tail behaviour , Random

Let eta(1), eta(2),& mldr; be independent copies of a random variable eta with zero mean and finite variance which is bounded from the right, that is, eta <= b almost surely for some b > 0. Considering different types of the asymptotic behaviour of the probability P {eta is an element of [b - x,b]} as x -> 0+, we derive precise tail asymptotics of the random Dirichlet series & sum;(k >= 1 )k(-alpha)eta(k) for alpha is an element of (1/2,1].

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