An Application of Renewal Theorems to Exponential Moments of Local Times
Leif Doering, Mladen Savov
TL;DR
This paper uses renewal theorems to analyze the exponential moments of local times, providing simplified proofs and stronger results on their asymptotic behavior.
Contribution
It introduces a renewal-theoretic approach to understand the asymptotics of exponential moments of local times, improving existing results.
Findings
Simplified proofs of known asymptotic behaviors.
Strengthened results on the asymptotic properties.
Clarified the transition phenomena in moment generating functions.
Abstract
In this note we explain two transitions known for moment generating functions of local times by means of properties of the renewal measure of a related renewal equation. The arguments simplify and strengthen results on the asymptotic behavior in the literature.
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Taxonomy
TopicsStochastic processes and statistical mechanics · stochastic dynamics and bifurcation · Stochastic processes and financial applications