Local limit theorem for the maximum of asymptotically stable random walks

DOI10.1007/s00440-010-0326-3zbMath1237.60039OpenAlexW2056842008MaRDI QIDQ2428508

Vitali Wachtel

Publication date: 26 April 2012

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://opus.bibliothek.uni-augsburg.de/opus4/files/54971/54971.pdf

zbMATH Keywords

random walkslimit theoremsrenewal theorem

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Sums of independent random variables; random walks (60G50) Stable stochastic processes (60G52) Renewal theory (60K05)

Related Items (4)

Almost invariance of distributions for random walks on groups ⋮ Local behaviour of first passage probabilities ⋮ The entropic Erdős-Kac limit theorem ⋮ First-Passage Times over Moving Boundaries for Asymptotically Stable Walks

Cites Work

• Unnamed Item
• Invariance principles for random walks conditioned to stay positive
• Local probabilities for random walks conditioned to stay positive
• One-sided local large deviation and renewal theorems in the case of infinite mean
• The asymptotic behavior of densities related to the supremum of a stable process
• Estimating the rate of convergence for the distribution of the maximum sums of independent random quantities
• Random walks and Riesz kernels
• A discrete renewal theorem with infinite mean
• On a Local Limit Theorem for the Maximum of Sums of Independent Random Variables
• Wiener – hopf factorization revisited and some applications
• On the local behaviour of ladder height distributions

This page was built for publication: Local limit theorem for the maximum of asymptotically stable random walks