On decay–surge population models

@article{Goncalves2020OnDP,
  title={On decay–surge population models},
  author={Branda Goncalves and Thierry Huillet and Eva L{\"o}cherbach},
  journal={Advances in Applied Probability},
  year={2020}
}
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… 
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References

SHOWING 1-10 OF 28 REFERENCES

On population growth with catastrophes

Abstract In this article, we study a particular class of Piecewise deterministic Markov processes (PDMP’s) which are semi-stochastic catastrophe versions of deterministic population growth models. In

A Markovian growth-collapse model

We consider growth-collapse processes (GCPs) that grow linearly between random partial collapse times, at which they jump down according to some distribution depending on their current level. The

Persistence times of populations with large random fluctuations.

  • F. Hanson
  • Mathematics
    Theoretical population biology
  • 1978

On some tractable growth-collapse processes with renewal collapse epochs

In this paper we generalize existing results for the steady-state distribution of growth-collapse processes with independent exponential intercollapse times to the case where they have a general

Nonlinear Shot Noise: From aggregate dynamics to maximal dynamics

We consider Nonlinear Shot Noise systems in which external shots hit the system following an arbitrary Poissonian inflow and, after impact, dissipate to zero governed by an arbitrary nonlinear decay

On Growth-Collapse Processes with Stationary Structure and Their Shot-Noise Counterparts

  • O. Kella
  • Mathematics
    Journal of Applied Probability
  • 2009
In this paper we generalize existing results for the steady-state distribution of growth-collapse processes. We begin with a stationary setup with some relatively general growth process and observe

A stationary distribution for the growth of a population subject to random catastrophes

The problem of the existence of a stationary distribution and the convergence towards it in a certain semistochastic model for the growth of a population and a constructive method for finding the stationary distribution is given.

The maximal process of nonlinear shot noise

Piecewise-deterministic Markov Processes: A General Class of Non-diffusion Stochastic Models

Stochastic calculus for these stochastic processes is developed and a complete characterization of the extended generator is given; this is the main technical result of the paper.