Occupation Times of General Lévy Processes

Lan Wu, Jiang Zhou () and Shuang Yu
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Lan Wu: Peking University
Jiang Zhou: Peking University
Shuang Yu: Peking University

Journal of Theoretical Probability, 2017, vol. 30, issue 4, 1565-1604

Abstract: 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.

Keywords: Occupation times; Lévy processes; Laplace transform; Infinitely divisible distribution; Strong Markov property; Continuity theorem; 60G51 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10959-016-0690-8

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