Perpetual Integrals for Levy Processes
Leif Doering, Andreas E. Kyprianou
TL;DR
This paper investigates the conditions under which perpetual integrals of Levy processes are almost surely finite, extending zero-one laws known for Brownian motion and spectrally one-sided Levy processes using fluctuation theory.
Contribution
It establishes necessary and sufficient conditions for the finiteness of perpetual integrals of Levy processes, generalizing existing zero-one laws.
Findings
Zero-one law for Levy processes with local times
Necessary and sufficient conditions for finiteness of perpetual integrals
Extension of known results from Brownian motion to Levy processes
Abstract
We ask for necessary and sufficient conditions for almost sure finiteness of the perpetual integrals of a Levy process. Zero-one laws are already known for Brownian motion with drift and spectrally one-sided Levy processes. Under the assumption that local times exist, we use fluctuation theory and Jeulin's lemma to prove the zero-one law.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStochastic processes and financial applications · Stochastic processes and statistical mechanics · Complex Systems and Time Series Analysis