Integral Functionals for Spectrally Positive Lévy Processes

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 cl...

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Bibliographic Details
Published in:Journal of theoretical probability 2023-03, Vol.36 (1), p.297-314
Main Authors: Li, Pei-Sen, Zhou, Xiaowen
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
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Summary: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.
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-022-01176-y