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Observing Stochastic Processes, and Approximate Transform Inversion

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  • D. P. Gaver

    (Carnegie Institute of Technology and Westinghouse Electric Co., Pittsburgh, Pennsylvania)

Abstract

This paper describes a method for obtaining numerical information concerning the time-dependent behavior of stochastic processes such as those arising in queuing theory. The method leads to an approximate inverse of the Laplace transform. Examples are given of applications to transforms with known inverses, and the evolution of expected waiting time at a simple single-server queue is illustrated, both when there is a stationary solution and in the saturated case.

Suggested Citation

  • D. P. Gaver, 1966. "Observing Stochastic Processes, and Approximate Transform Inversion," Operations Research, INFORMS, vol. 14(3), pages 444-459, June.
    • Handle: RePEc:inm:oropre:v:14:y:1966:i:3:p:444-459
    DOI: 10.1287/opre.14.3.444
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    Cited by:

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    9. Ibrahim Ayuba & Lateef T. Akanji & Jefferson L. Gomes & Gabriel K. Falade, 2021. "Investigation of Drift Phenomena at the Pore Scale during Flow and Transport in Porous Media," Mathematics, MDPI, vol. 9(19), pages 1-36, October.
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    11. Kimura, Toshikazu, 2010. "Valuing continuous-installment options," European Journal of Operational Research, Elsevier, vol. 201(1), pages 222-230, February.
    12. Raoofian Naeeni, M. & Campagna, R. & Eskandari-Ghadi, M. & Ardalan, Alireza A., 2015. "Performance comparison of numerical inversion methods for Laplace and Hankel integral transforms in engineering problems," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 759-775.
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    14. Landriault, David & Willmot, Gordon, 2008. "On the Gerber-Shiu discounted penalty function in the Sparre Andersen model with an arbitrary interclaim time distribution," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 600-608, April.
    15. Joseph Abate & Ward Whitt, 2006. "A Unified Framework for Numerically Inverting Laplace Transforms," INFORMS Journal on Computing, INFORMS, vol. 18(4), pages 408-421, November.
    16. Qu, Yan & Dassios, Angelos & Zhao, Hongbiao, 2021. "Random variate generation for exponential and gamma tilted stable distributions," LSE Research Online Documents on Economics 108593, London School of Economics and Political Science, LSE Library.
    17. Wu, Bei & Zhang, Yamei & Zhao, Songzheng, 2023. "Modeling coupled effects of dynamic environments and zoned shocks on systems under dependent failure processes," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    18. Jingyuan Shen & Alaa Elwany & Lirong Cui, 2018. "Reliability modeling for systems degrading in K cyclical regimes based on gamma processes," Journal of Risk and Reliability, , vol. 232(6), pages 754-765, December.
    19. Leippold, Markus & Vasiljević, Nikola, 2017. "Pricing and disentanglement of American puts in the hyper-exponential jump-diffusion model," Journal of Banking & Finance, Elsevier, vol. 77(C), pages 78-94.
    20. Lateef T. Akanji & Gabriel K. Falade, 2018. "Closed-Form Solution of Radial Transport of Tracers in Porous Media Influenced by Linear Drift," Energies, MDPI, vol. 12(1), pages 1-29, December.
    21. Hofert, Marius, 2008. "Sampling Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5163-5174, August.
    22. Efstathios Avdis & Ward Whitt, 2007. "Power Algorithms for Inverting Laplace Transforms," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 341-355, August.
    23. A. Baykal Hafızoğlu & Esma S. Gel & Pınar Keskinocak, 2013. "Expected Tardiness Computations in Multiclass Priority M / M / c Queues," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 364-376, May.
    24. Wei, Xiaohua & Bai, Sijun & Wu, Bei, 2023. "A novel shock-dependent preventive maintenance policy for degraded systems subject to dynamic environments and N-critical shocks," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    25. Gatto, Riccardo, 2013. "The von Mises–Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1669-1676.

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