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The stochastic fluid–fluid model: A stochastic fluid model driven by an uncountable-state process, which is a stochastic fluid model itself

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  • Bean, Nigel G.
  • O’Reilly, Małgorzata M.

Abstract

We introduce the Stochastic Fluid–Fluid Model, which offers powerful modeling ability for a wide range of real-life systems of significance. We first derive the infinitesimal generator, with respect to time, of the driving stochastic fluid model. We then use this to derive the infinitesimal generator of a particular Laplace–Stieltjes transform of the model, which is the foundation of our analysis. We develop expressions for the Laplace–Stieltjes transforms of various performance measures for the transient and limiting analysis of the model. This work is the first direct analysis of a stochastic fluid model that is Markovian on a continuous state space.

Suggested Citation

  • Bean, Nigel G. & O’Reilly, Małgorzata M., 2014. "The stochastic fluid–fluid model: A stochastic fluid model driven by an uncountable-state process, which is a stochastic fluid model itself," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1741-1772.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:5:p:1741-1772
    DOI: 10.1016/j.spa.2013.12.006
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    References listed on IDEAS

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    1. Bean, Nigel G. & O'Reilly, Malgorzata M. & Taylor, Peter G., 2005. "Hitting probabilities and hitting times for stochastic fluid flows," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1530-1556, September.
    2. D. R. Bellwood & T. P. Hughes & C. Folke & M. Nyström, 2004. "Confronting the coral reef crisis," Nature, Nature, vol. 429(6994), pages 827-833, June.
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    Cited by:

    1. Samuelson, Aviva & Haigh, Andrew & O'Reilly, Małgorzata M. & Bean, Nigel G., 2017. "Stochastic model for maintenance in continuously deteriorating systems," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1169-1179.
    2. Nigel Bean & Angus Lewis & Giang T. Nguyen & Małgorzata M. O’Reilly & Vikram Sunkara, 2022. "A Discontinuous Galerkin Method for Approximating the Stationary Distribution of Stochastic Fluid-Fluid Processes," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2823-2864, December.
    3. Nikki Sonenberg & Peter G. Taylor, 2019. "Networks of interacting stochastic fluid models with infinite and finite buffers," Queueing Systems: Theory and Applications, Springer, vol. 92(3), pages 293-322, August.

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