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A growth–collapse model: Lévy inflow, geometric crashes, and generalized Ornstein–Uhlenbeck dynamics

Author

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  • Eliazar, Iddo
  • Klafter, Joseph

Abstract

We introduce and study a stochastic growth–collapse model. The growth process is a steady random inflow with stationary, independent, and non-negative increments. Crashes occur according to an arbitrary renewal process, they are geometric, and their magnitudes are random and are governed by an arbitrary distribution on the unit interval. If the system's pre-crash level is X>0, and the crash magnitude is 0

Suggested Citation

  • Eliazar, Iddo & Klafter, Joseph, 2004. "A growth–collapse model: Lévy inflow, geometric crashes, and generalized Ornstein–Uhlenbeck dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 1-21.
    • Handle: RePEc:eee:phsmap:v:334:y:2004:i:1:p:1-21
    DOI: 10.1016/j.physa.2003.11.007
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    Cited by:

    1. Huillet, Thierry E., 2011. "On a Markov chain model for population growth subject to rare catastrophic events," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4073-4086.
    2. Onno Boxma & Michel Mandjes, 2021. "Shot-noise queueing models," Queueing Systems: Theory and Applications, Springer, vol. 99(1), pages 121-159, October.

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