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Integral Functionals for Spectrally Positive Lévy Processes

Author

Listed:
  • Pei-Sen Li

    (Beijing Institute of Technology)

  • Xiaowen Zhou

    (Concordia University)

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.

Suggested Citation

  • Pei-Sen Li & Xiaowen Zhou, 2023. "Integral Functionals for Spectrally Positive Lévy Processes," Journal of Theoretical Probability, Springer, vol. 36(1), pages 297-314, March.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:1:d:10.1007_s10959-022-01176-y
    DOI: 10.1007/s10959-022-01176-y
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    References listed on IDEAS

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    1. Li, Pei-Sen, 2019. "A continuous-state polynomial branching process," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2941-2967.
    2. J. C. Pardo, 2009. "The Upper Envelope of Positive Self-Similar Markov Processes," Journal of Theoretical Probability, Springer, vol. 22(2), pages 514-542, June.
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