Local large deviations and the strong renewal theorem

DOI10.1214/19-EJP319zbMath1467.60068arXiv1612.07635OpenAlexW3102248533MaRDI QIDQ2316596

Francesco Caravenna, Ronald Arthur Doney

Publication date: 6 August 2019

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.07635

zbMATH Keywords

regular variationlocal limit theoremrenewal theorem

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Large deviations (60F10) Renewal theory (60K05)

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Cites Work

• Unnamed Item
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• Disorder and critical phenomena through basic probability models. École d'Été de Probabilités de Saint-Flour XL -- 2010.
• One-sided local large deviation and renewal theorems in the case of infinite mean
• Spitzer's condition for random walks and Lévy processes
• The left tail of renewal measure
• On the ladder heights of random walks attracted to stable laws of exponent 1
• On a multivariate strong renewal theorem
• A renewal theorem in the infinite mean case
• Infinite measure mixing for some mechanical systems
• Contact process under renewals I
• Strong renewal theorems with infinite mean beyond local large deviations
• Random walks and Riesz kernels
• A discrete renewal theorem with infinite mean
• Strong renewal theorems and local large deviations for multivariate random walks and renewals
• The continuum disordered pinning model
• First-Passage Times over Moving Boundaries for Asymptotically Stable Walks
• Infinite measure renewal theorem and related results
• Implicit renewal theory in the arithmetic case
• Strong Renewal Theorems with Infinite Mean
• A renewal theorem for distributions on 𝑅¹ without expectation
• Large deviations of sums of independent random variables

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