Upper functions for lÉvy processes having only negative jumps

Y. K. Kim; In-Suk Wee

doi:10.1080/07362999108809242

Upper functions for lÉvy processes having only negative jumps

Y. K. Kim, In-Suk Wee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Let X_t, t ≥ 0 be a real valued process with stationary independent increments having only negative jumps. We obtain b(t) such that lim sup X_t/b(t) equals a finite positive constant with probability one as t → 0 and t → ∞ under extra condition. The hypotheses about the behavior of Lévy measure near zero and infinity are necessary to guarantee that the lim sup is positive.

Original language	English
Pages (from-to)	301-310
Number of pages	10
Journal	Stochastic Analysis and Applications
Volume	9
Issue number	3
DOIs	https://doi.org/10.1080/07362999108809242
Publication status	Published - 1991 Jan 1

ASJC Scopus subject areas

Statistics, Probability and Uncertainty
Applied Mathematics
Statistics and Probability

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10.1080/07362999108809242

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abstract = "Let Xt, t ≥ 0 be a real valued process with stationary independent increments having only negative jumps. We obtain b(t) such that lim sup Xt/b(t) equals a finite positive constant with probability one as t → 0 and t → ∞ under extra condition. The hypotheses about the behavior of L{\'e}vy measure near zero and infinity are necessary to guarantee that the lim sup is positive.",

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AB - Let Xt, t ≥ 0 be a real valued process with stationary independent increments having only negative jumps. We obtain b(t) such that lim sup Xt/b(t) equals a finite positive constant with probability one as t → 0 and t → ∞ under extra condition. The hypotheses about the behavior of Lévy measure near zero and infinity are necessary to guarantee that the lim sup is positive.

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Upper functions for lÉvy processes having only negative jumps

Abstract

ASJC Scopus subject areas

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