Subexponential densities of compound Poisson sums and the supremum of a random walk

DOI10.1215/21562261-2022-0041OpenAlexW3004335998MaRDI QIDQ2685120

Takaaki Shimura, Toshiro Watanabe

Publication date: 19 February 2023

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.11362

zbMATH Keywords

random walksubexponential densitylocal subexponentialitycompound Poisson sum

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Sums of independent random variables; random walks (60G50)

Related Items (1)

Subexponentialiy of densities of infinitely divisible distributions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local subexponentiality and self-decomposability
• Subexponential densities of infinitely divisible distributions on the half-line
• Convolution equivalence and distributions of random sums
• Ratio of the tail of an infinitely divisible distribution on the line to that of its Lévy measure
• Subexponential distributions and characterizations of related classes
• Functions of probability measures
• Asymptotics for sums of random variables with local subexponential behaviour
• A local limit theorem for random walk maxima with heavy tails
• The maximum on a random time interval of a random walk with long-tailed increments and negative drift.
• Two hypotheses on the exponential class in the class of \(O\)-subexponential infinitely divisible distributions
• The Wiener condition and the conjectures of Embrechts and Goldie
• Subexponential distributions and integrated tails
• An Introduction to Heavy-Tailed and Subexponential Distributions
• SECOND ORDER SUBEXPONENTIALITY AND INFINITE DIVISIBILITY
• Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues

This page was built for publication: Subexponential densities of compound Poisson sums and the supremum of a random walk