Law and exact sampling of the first passage of a spectrally positive strictly stable process

Zhiyi Chi

Published 2018-01-21Version 1

For a spectrally positive and strictly stable process with index in (1, 2), a series representation is obtained for the joint distribution of the "first passage triplet", i.e., the time, the undershoot, and the overshoot of first passage. The representation is shown to allow exact sampling of the first passage triplet. Consequences of the representation include the joint law of the value and the running maximum of the process at a fixed time point, and a joint law of the first passage triplet and the running maximum before the first passage.