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1 results

  • On decay–surge population models

  • Part of
  • Branda Goncalves, Thierry Huillet, Eva Löcherbach
  • Journal:
    Advances in Applied Probability / Volume 55 / Issue 2 / June 2023
    Published online by Cambridge University Press:
    08 November 2022, pp. 444-472
    Print publication:
    June 2023
    • Article
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  • We consider continuous space–time decay–surge population models, which are semi-stochastic processes for which deterministically declining populations, bound to fade away, are reinvigorated at random times by bursts or surges of random sizes. In a particular separable framework (in a sense made precise below) we provide explicit formulae for the scale (or harmonic) function and the speed measure of the process. The behavior of the scale function at infinity allows us to formulate conditions under which such processes either explode or are transient at infinity, or Harris recurrent. A description of the structures of both the discrete-time embedded chain and extreme record chain of such continuous-time processes is supplied.