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arXiv · 1604.00097

Occupation times of general L\'evy processes

Lan Wu·Jiang Zhou·Shuang Yu
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Abstract

For an arbitrary L\'evy 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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Lan Wu, Jiang Zhou, Shuang Yu. 2016-04-01. Occupation times of general L\'evy processes. https://arxiv.org/abs/1604.00097

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