Convolution powers of unbounded measures on the positive half-line

Autor:	Buraczewski, Dariusz, Iksanov, Alexander, Marynych, Alexander
Rok vydání:	2024
Předmět:	Mathematics - Probability Mathematics - Classical Analysis and ODEs Primary: 60F10 Secondary: 44A35 60J80
Druh dokumentu:	Working Paper
Popis:	For a right-continuous nondecreasing and unbounded function $V$ of at most exponential growth, which vanishes on the negative halfline, we investigate the asymptotic behavior of the Lebesgue-Stieltjes convolution powers $V^{\ast(j)}(t)$ as both $j$ and $t$ tend to infinity. We obtain a comprehensive asymptotic formula for $V^{\ast(j)}(t)$, which is valid across different regimes of simultaneous growth of $j$ and $t$. Our main technical tool is an exponential change of measure, which is a standard technique in the large deviations theory. Various applications of our result are given. Comment: 21 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.04955 Zobrazit plný text záznamu View this record from Arxiv