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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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    12. Kimura, Toshikazu, 2010. "Valuing continuous-installment options," European Journal of Operational Research, Elsevier, vol. 201(1), pages 222-230, February.
    13. Tan, Zhizhong & Wu, Bei & Che, Ada, 2023. "Resilience modeling for multi-state systems based on Markov processes," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    14. 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.
    15. Kenkre, V.M. & Spendier, K., 2022. "A theory of coalescence of signaling receptor clusters in immune cells," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).
    16. Razminia, Kambiz & Razminia, Abolhassan & Torres, Delfim F.M., 2015. "Pressure responses of a vertically hydraulic fractured well in a reservoir with fractal structure," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 374-380.
    17. Ballestra, Luca Vincenzo & Pacelli, Graziella & Radi, Davide, 2020. "Modeling CDS spreads: A comparison of some hybrid approaches," Journal of Empirical Finance, Elsevier, vol. 57(C), pages 107-124.
    18. 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).
    19. Hofert, Marius, 2008. "Sampling Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5163-5174, August.
    20. Efstathios Avdis & Ward Whitt, 2007. "Power Algorithms for Inverting Laplace Transforms," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 341-355, August.
    21. 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).
    22. Qinglai Dong & Lirong Cui & Hongda Gao, 2019. "A bivariate replacement policy for an imperfect repair system based on geometric processes," Journal of Risk and Reliability, , vol. 233(4), pages 670-681, August.
    23. Li, Na & Stanford, David A. & Sharif, Azaz B. & Caron, Richard J. & Pardhan, Alim, 2019. "Optimising key performance indicator adherence with application to emergency department congestion," European Journal of Operational Research, Elsevier, vol. 272(1), pages 313-323.
    24. 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.
    25. 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.

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