# Occupation Times of General Lévy Processes

@article{Wu2016OccupationTO, title={Occupation Times of General L{\'e}vy Processes}, author={Lan Wu and Jiang Zhou and Shuang Yu}, journal={Journal of Theoretical Probability}, year={2016}, volume={30}, pages={1565-1604} }

For an arbitrary Lévy process X which is not a compound Poisson process, we are interested in its occupation times. We use a quite novel and useful approach to derive formulas for the Laplace transform of the joint distribution of X and its occupation times. Our formulas are compact, and more importantly, the forms of the formulas clearly demonstrate the essential quantities for the calculation of occupation times of X. It is believed that our results are important not only for the study of…

#### 4 Citations

Occupation times of Lévy processes

- MathematicsInternational Journal of Financial Engineering
- 2021

In this paper, we give a complete and succinct proof that an explicit formula for the occupation time holds for all Lévy processes, which is important to the pricing problems of various…

Occupation times of alternating renewal processes with Lévy applications

- Computer Science, MathematicsJournal of Applied Probability
- 2018

A central limit theorem is established (entailing that a centered and normalized version of α(t)∕t converges to a zero-mean normal random variable as t→∞) and the tail asymptotics of ℙ(α( t)√t≥q) are established.

On weighted occupation times for refracted spectrally negative Lévy processes

- Physics, MathematicsJournal of Mathematical Analysis and Applications
- 2018

Abstract For refracted spectrally negative Levy processes, we identify expressions for several quantities related to the Laplace transforms of their weighted occupation times until first exit times.…

Alternative approach to derive q-potential measures of refracted spectrally L\'evy processes

- Mathematics
- 2016

For a refracted L\'evy process driven by a spectrally negative L\'evy process, we use a different approach to derive expressions for its q-potential measures without killing. Unlike previous methods…

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