On the rate of growth of Lévy processes with no positive jumps conditioned to stay positive. (English) Zbl 1189.60099

Pardo Millan, Juan Carlos

Electron. Commun. Probab. 13, 494-506 (2008).

Summary: We study the asymptotic behaviour of Lévy processes with no positive jumps conditioned to stay positive and some related processes. In particular, we establish an integral test for the lower envelope at 0 and at \(+\infty\) and an analogue of Khintchin’s law of the iterated logarithm at 0 and at \(+\infty\), for the upper envelope of the reflected process at its future infimum.

MSC:

60G51	Processes with independent increments; Lévy processes
60G17	Sample path properties
60E07	Infinitely divisible distributions; stable distributions

Keywords:

Lévy processes conditioned to stay positive; future infimum process; first and last passage times; occupation times; rate of growth; integral tests