Integral functionals for spectrally positive Levy processes
Pei-Sen Li, Xiaowen Zhou
TL;DR
This paper establishes criteria for the almost sure finiteness of integral functionals of spectrally positive Lévy processes and applies these results to analyze extinction and explosion in nonlinear branching processes.
Contribution
It provides new necessary and sufficient conditions for the finiteness of integral functionals and links these to extinction and explosion behaviors via Lamperti transforms.
Findings
Criteria for almost sure finiteness of integral functionals.
New integral tests for extinction and explosion behaviors.
Application to continuous-state nonlinear branching processes.
Abstract
We find necessary and sufficient conditions for almost sure finiteness of integral functionals of spectrally positive L\'evy processes. 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.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Stochastic processes and financial applications · Advanced Queuing Theory Analysis