The distribution and asympotic behaviour of the negative Wiener–Hopf factor for Lévy processes with rational positive jumps
Keyword(s):
AbstractWe study the distribution of the negative Wiener–Hopf factor for a class of two-sided jump Lévy processes whose positive jumps have a rational Laplace transform. The positive Wiener–Hopf factor for this class of processes was studied by Lewis and Mordecki (2008). Here we obtain a formula for the Laplace transform of the negative Wiener–Hopf factor, as well as an explicit expression for its probability density in terms of sums of convolutions of known functions. Under additional regularity conditions on the Lévy measure of the studied processes, we also provide asymptotic results as $u\to-\infty$ for the distribution function F(u) of the negative Wiener–Hopf factor. We illustrate our results in some particular examples.
2004 ◽
Vol 41
(04)
◽
pp. 1191-1198
◽
Keyword(s):
2004 ◽
Vol 41
(4)
◽
pp. 1191-1198
◽
Keyword(s):
2016 ◽
Vol 19
(02)
◽
pp. 1650011
◽
2016 ◽
Vol 17
(05)
◽
pp. 1750033
◽
2009 ◽
Vol 79
(13)
◽
pp. 1501-1508
◽
2010 ◽
Vol 47
(04)
◽
pp. 1023-1033
◽
2006 ◽
Vol 38
(03)
◽
pp. 768-791
◽
Keyword(s):
2011 ◽
Vol 14
(07)
◽
pp. 1045-1090
◽
Keyword(s):
1992 ◽
Vol 29
(03)
◽
pp. 499-518
◽