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Some excursion calculations for spectrally one-sided Lévy processes. (English) Zbl 1068.60073
Émery, Michel (ed.) et al., 38th seminar on probability. Dedicated Jacques Azéma on the occasion on his 65th birthday. Berlin: Springer (ISBN 3-540-23973-1/pbk). Lecture Notes in Mathematics 1857, 5-15 (2005).
Let \(Y\) and \({\hat {Y}}\) be the reflected processes from bottom and from above, respectively, of a Lévy process without positive jumps and having neither a pure drift nor the negative of a subordinator. The theorem of M. R. Pistorius [J. Theor. Probab. 17, No. 1, 183–220 (2004; Zbl 1049.60042)] gives the \(q\)-resolvent densities of \(Y\) and \({\hat {Y}} \) killed on exiting interval \([0,a]\). In the present paper, this result is re-established by direct excursion theory calculation.
For the entire collection see [Zbl 1055.60001].

MSC:
60G51 Processes with independent increments; Lévy processes
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