Two-sided exit problem for a Spectrally Negative α-Stable Ornstein-Uhlenbeck Process and the Wright's generalized hypergeometric functions
Pierre Patie, IMSV - University of Bern
Abstract
The Laplace transform of the first
exit time from a finite interval by a regular spectrally negative
α-stable Ornstein-Uhlenbeck process
is provided in terms of the Wright's generalized hypergeometric
function. The Laplace transform of first passage
times is also derived for some related processes such as the
process killed when it enters the negative half line and the
process conditioned to stay positive. The law of the maximum of
the associated bridges is computed in terms of the q-resolvent
density. As a byproduct, we deduce some interesting analytical properties for some Wright's generalized hypergeometric functions.
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