Seminar series
Date
Mon, 09 Feb 2004
15:45
15:45
Location
DH 3rd floor SR
Speaker
Martijn Pistorius
Organisation
King's College, London
Consider a spectrally one-sided Levy process X and reflect it at
its past infimum I. Call this process Y. We determine the law of the
first crossing time of Y of a positive level a in terms of its
'scale' functions. Next we study the exponential decay of the
transition probabilities of Y killed upon leaving [0,a]. Restricting
ourselves to the case where X has absolutely continuous transition
probabilities, we also find the quasi-stationary distribution of
this killed process. We construct then the process Y confined in
[0,a] and prove some properties of this process.