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Processes with catastrophes: Large deviation point of view

Author

Listed:
  • Logachov, A.
  • Logachova, O.
  • Yambartsev, A.

Abstract

In this paper, we propose a new definition of catastrophes and present our results on large deviations for Poisson processes with catastrophes that satisfy this definition. Our earlier work focused on (almost) uniformly distributed catastrophes, but the current paper extends the results to a larger class of catastrophes. We show that the rate function remains the same regardless of the distribution of catastrophic events. Additionally, we extend and generalize our previous results on the limiting behavior of the supremum of the considered processes.

Suggested Citation

  • Logachov, A. & Logachova, O. & Yambartsev, A., 2024. "Processes with catastrophes: Large deviation point of view," Stochastic Processes and their Applications, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:spapps:v:176:y:2024:i:c:s0304414924001534
    DOI: 10.1016/j.spa.2024.104447
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