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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465233474

Digital Object Identifier
doi:10.1214/ECP.v13-1414

Mathematical Reviews number (MathSciNet)
MR2447836

Zentralblatt MATH identifier
1189.60099

Subjects
Primary: 60 G 17
Secondary: 60 G 51

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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