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Algorithms for the Laplace–Stieltjes Transforms of First Return Times for Stochastic Fluid Flows

Author

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  • Nigel G. Bean

    (University of Adelaide)

  • Małgorzata M. O’Reilly

    (University of Tasmania)

  • Peter G. Taylor

    (University of Melbourne)

Abstract

We derive several algorithms, including quadratically convergent algorithms, which can be used to calculate the Laplace–Stieltjes transforms of the time taken to return to the initial level in the Markovian stochastic fluid flow model. We give physical interpretations of the algorithms and consider their numerical analysis. The numerical performance of the algorithms, which depends on the physical properties of the process, is discussed and illustrated with simple examples. Besides the powerful algorithms, this paper contributes interesting theoretical results. In particular, the methodology for constructing these algorithms is a valuable contribution to the theory of fluid flow models. Moreover, useful physical interpretations of the algorithms, and related expressions, given in terms of the fluid flow model, can assist in further analysis and help in a better understanding of the model.

Suggested Citation

  • Nigel G. Bean & Małgorzata M. O’Reilly & Peter G. Taylor, 2008. "Algorithms for the Laplace–Stieltjes Transforms of First Return Times for Stochastic Fluid Flows," Methodology and Computing in Applied Probability, Springer, vol. 10(3), pages 381-408, September.
    • Handle: RePEc:spr:metcap:v:10:y:2008:i:3:d:10.1007_s11009-008-9077-3
    DOI: 10.1007/s11009-008-9077-3
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    References listed on IDEAS

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    1. Joseph Abate & Ward Whitt, 1995. "Numerical Inversion of Laplace Transforms of Probability Distributions," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 36-43, February.
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    Cited by:

    1. Sarah Dendievel & Guy Latouche, 2017. "Approximations for Time-Dependent Distributions in Markovian Fluid Models," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 285-309, March.

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