Convolution powers of unbounded measures on the positive half-line

2024/04/07 by Dariusz Buraczewski, Buraczewski, Dariusz, Alexander Iksanov +3 · 1 citation
Mathematics · #60J80 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary: 60F10 #Probability (math.PR) #Secondary: 44A35 #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2404.04955

openalex publication_date 2024/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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^∗(j)(t) as both j and t tend to infinity. We obtain a comprehensive asymptotic formula for V^∗(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.

Cited by

• On local large deviations for decoupled random walks

Related

• Convolution powers of complex functions on Z
• Almost everywhere convergence of convolution powers without finite second moment
• Measures of polynomial growth and classical convolution inequalities
• Convolution powers of complex functions on ℤ^d
• On the convolution powers of complex functions on Z