Abstract
We are interested in occupation times of Levy processes with jumps rational Laplace transforms. The corresponding boundary value problems via the Feynman-Kac representation are solved to obtain an explicit formula for the joint distribution of the occupation time and the terminal value of the Levy processes with jumps rational Laplace transforms.
Highlights
The occupation time is the amount of time a stochastic process stays with in a certain range
We are interested in occupation times of Lévy processes with jumps rational Laplace transforms
The corresponding boundary value problems via the Feynman-Kac representation are solved to obtain an explicit formula for the joint distribution of the occupation time and the terminal value of the Lévy processes with jumps rational Laplace transforms
Summary
The occupation time is the amount of time a stochastic process stays with in a certain range. Many explicit results on Laplace transforms for occupation times have been obtained for some well known examples of Lévy process. Lévy’s arcsine law is a well known result. It states the following, let Γ+(t) be the time W spends above 0 up to time t: t. Lévy [10] (for more details see Chapter IV of [16]) showed that for each t > 0 the variable Γ+(t)/t follows the arcsine law:. The investigation on occupation times of Lévy processes has made much great progress. We are interested in the joint Laplace transforms of X = (Xt)t≥0 and its occupation times, i.e,.
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