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

Authors
Publication Date
Source
Hal-Diderot
Keywords
• Lévy Processes Conditioned To Stay Positive
• Future Infimum Process
• First And Last Passage Times
• Rate Of Growth
• Integral Tests
• 60 G 17, 60 G 51.
• [Math.Math-Pr] Mathematics [Math]/Probability [Math.Pr]
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.