Occupation times of general Lévy processes

2016/04/01 by Lan Wu, Jiang Zhou, Wu, Lan +3
Decision Sciences · Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1604.00097

openalex publication_date 2016/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 stochastic processes, but also for financial applications.

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