Electronic Communications in Probability

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

Juan Carlos Pardo Millan

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In this note, 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.

Article information

Electron. Commun. Probab., Volume 13 (2008), paper no. 47, 494-506.

Accepted: 13 October 2008
First available in Project Euclid: 6 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60 G 17
Secondary: 60 G 51

Lévy processes conditioned to stay positive Future infimum process First and last passage times Occupation times Rate of growth Integral tests

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Pardo Millan, Juan Carlos. On the rate of growth of Lévy processes with no positive jumps conditioned to stay positive. Electron. Commun. Probab. 13 (2008), paper no. 47, 494--506. doi:10.1214/ECP.v13-1414. https://projecteuclid.org/euclid.ecp/1465233474

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