Moments of passage times for Lévy processes

R. A. Doney; Ross A. Maller

doi:10.1016/j.anihpb.2003.10.005

Moments of passage times for Lévy processes

R. A. Doney, Ross A. Maller^*

^*Corresponding author for this work

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

21 Citations (Scopus)

Abstract

We give necessary and sufficient conditions, in terms of characteristics of the process, for finiteness of moments of passage times of general Lévy processes above horizontal, linear or certain curved boundaries. They apply in particular to processes which drift almost surely to infinity, and lead to estimates of the rate of growth of certain expectations, constituting generalised kinds of renewal theorems. Further results concern the inverse local time at the maximum and the ladder height process, the amount of time spent below a given level, and the overall minimum of the Lévy process.

Original language	English
Pages (from-to)	279-297
Number of pages	19
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	40
Issue number	3
DOIs	https://doi.org/10.1016/j.anihpb.2003.10.005
Publication status	Published - May 2004

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10.1016/j.anihpb.2003.10.005

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title = "Moments of passage times for L{\'e}vy processes",

abstract = "We give necessary and sufficient conditions, in terms of characteristics of the process, for finiteness of moments of passage times of general L{\'e}vy processes above horizontal, linear or certain curved boundaries. They apply in particular to processes which drift almost surely to infinity, and lead to estimates of the rate of growth of certain expectations, constituting generalised kinds of renewal theorems. Further results concern the inverse local time at the maximum and the ladder height process, the amount of time spent below a given level, and the overall minimum of the L{\'e}vy process.",

keywords = "Curved boundaries, Drift to infinity, Horizontal boundaries, Ladder height processes, Local time, Passage times of L{\'e}vy processes, Renewal theorems, Strong laws",

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T1 - Moments of passage times for Lévy processes

AU - Doney, R. A.

AU - Maller, Ross A.

PY - 2004/5

Y1 - 2004/5

N2 - We give necessary and sufficient conditions, in terms of characteristics of the process, for finiteness of moments of passage times of general Lévy processes above horizontal, linear or certain curved boundaries. They apply in particular to processes which drift almost surely to infinity, and lead to estimates of the rate of growth of certain expectations, constituting generalised kinds of renewal theorems. Further results concern the inverse local time at the maximum and the ladder height process, the amount of time spent below a given level, and the overall minimum of the Lévy process.

AB - We give necessary and sufficient conditions, in terms of characteristics of the process, for finiteness of moments of passage times of general Lévy processes above horizontal, linear or certain curved boundaries. They apply in particular to processes which drift almost surely to infinity, and lead to estimates of the rate of growth of certain expectations, constituting generalised kinds of renewal theorems. Further results concern the inverse local time at the maximum and the ladder height process, the amount of time spent below a given level, and the overall minimum of the Lévy process.

KW - Curved boundaries

KW - Drift to infinity

KW - Horizontal boundaries

KW - Ladder height processes

KW - Local time

KW - Passage times of Lévy processes

KW - Renewal theorems

KW - Strong laws

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U2 - 10.1016/j.anihpb.2003.10.005

DO - 10.1016/j.anihpb.2003.10.005

M3 - Article

SN - 0246-0203

VL - 40

SP - 279

EP - 297

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 3

ER -

Moments of passage times for Lévy processes

Abstract

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