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

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Publication Date
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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]
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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.

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