Suprema and sojourn times of Lévy processes with exponential tails

Michael Braverman

doi:10.1016/S0304-4149(97)00031-8

Suprema and sojourn times of Lévy processes with exponential tails

Michael Braverman

Department of Mathematics

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

15 Scopus citations

Abstract

We study the tail behaviour of the supremum of sample paths of Lévy process with exponential tail of the Lévy measure. Our approach is based on the theory of sojourn times developed by S. Berman. It allows us to compute the value of the limit of the ratio P(sup_{0 ≤ t ≤ l} X(t) > x)/p(x, ∞) as x → ∞, where ρ is the Lévy measure of the process.

Original language	English
Pages (from-to)	265-283
Number of pages	19
Journal	Stochastic Processes and their Applications
Volume	68
Issue number	2
DOIs	https://doi.org/10.1016/S0304-4149(97)00031-8
State	Published - 16 Jun 1997

Keywords

Exponential distributions
Lévy process
Sojourn times

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1016/S0304-4149(97)00031-8

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abstract = "We study the tail behaviour of the supremum of sample paths of L{\'e}vy process with exponential tail of the L{\'e}vy measure. Our approach is based on the theory of sojourn times developed by S. Berman. It allows us to compute the value of the limit of the ratio P(sup0 ≤ t ≤ l X(t) > x)/p(x, ∞) as x → ∞, where ρ is the L{\'e}vy measure of the process.",

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AB - We study the tail behaviour of the supremum of sample paths of Lévy process with exponential tail of the Lévy measure. Our approach is based on the theory of sojourn times developed by S. Berman. It allows us to compute the value of the limit of the ratio P(sup0 ≤ t ≤ l X(t) > x)/p(x, ∞) as x → ∞, where ρ is the Lévy measure of the process.

KW - Exponential distributions

KW - Lévy process

KW - Sojourn times

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ER -

Suprema and sojourn times of Lévy processes with exponential tails

Abstract

Keywords

ASJC Scopus subject areas

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