Integral Functionals for Spectrally Positive Lévy Processes

Pei Sen Li; Xiaowen Zhou

doi:10.1007/s10959-022-01176-y

Integral Functionals for Spectrally Positive Lévy Processes

Pei Sen Li, Xiaowen Zhou^*

^*Corresponding author for this work

School of Mathematics and Statistics

Concordia University

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

2 Citations (Scopus)

Abstract

We find necessary and sufficient conditions for almost sure finiteness of integral functionals of spectrally positive Lévy processes under conditional probabilities. Via Lamperti-type transforms, these results can be applied to obtain new integral tests on extinction and explosion behaviors for a class of continuous-state nonlinear branching processes.

Original language	English
Pages (from-to)	297-314
Number of pages	18
Journal	Journal of Theoretical Probability
Volume	36
Issue number	1
DOIs	https://doi.org/10.1007/s10959-022-01176-y
Publication status	Published - Mar 2023

Keywords

Continuous-state branching process
Explosion
Extinction
Integral test
Lamperti transform
Lévy process
Stochastic integral equation

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10.1007/s10959-022-01176-y

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Li, P. S., & Zhou, X. (2023). Integral Functionals for Spectrally Positive Lévy Processes. Journal of Theoretical Probability, 36(1), 297-314. https://doi.org/10.1007/s10959-022-01176-y

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abstract = "We find necessary and sufficient conditions for almost sure finiteness of integral functionals of spectrally positive L{\'e}vy processes under conditional probabilities. Via Lamperti-type transforms, these results can be applied to obtain new integral tests on extinction and explosion behaviors for a class of continuous-state nonlinear branching processes.",

keywords = "Continuous-state branching process, Explosion, Extinction, Integral test, Lamperti transform, L{\'e}vy process, Stochastic integral equation",

author = "Li, {Pei Sen} and Xiaowen Zhou",

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AU - Zhou, Xiaowen

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AB - We find necessary and sufficient conditions for almost sure finiteness of integral functionals of spectrally positive Lévy processes under conditional probabilities. Via Lamperti-type transforms, these results can be applied to obtain new integral tests on extinction and explosion behaviors for a class of continuous-state nonlinear branching processes.

KW - Continuous-state branching process

KW - Explosion

KW - Extinction

KW - Integral test

KW - Lamperti transform

KW - Lévy process

KW - Stochastic integral equation

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Integral Functionals for Spectrally Positive Lévy Processes

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Keywords

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