On the rate of growth of Lévy processes with no positive jumps conditioned to stay positive

Abstract

In this article, we study the asymptotic behaviour of Lévy processes with no positive jumps conditioned to stay positive. We establish integral tests for the lower envelope at 0 and at $+\infty$ and an analogue of Khintchin's law of the iterated logarithm at 0 and $+\infty$, for the upper envelope.