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On the level crossing of multi-dimensional delayed renewal processes

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  • Jewgeni H. Dshalalow

Abstract

The paper studies the behavior of an ( l + 3 ) th-dimensional, delayed renewal process with dependent components, the first three (called active ) of which are to cross one of their respective thresholds. More specifically, the crossing takes place when at least one of the active components reaches or exceeds its assigned level. The values of the other two active components, as well as the rest of the components ( passive ), are to be registered. The analysis yields the joint functional of the crossing level and other characteristics (some of which can be interpreted as the first passage time) in a closed form, refining earlier results of the author. A brief, informal discussion of various applications to stochastic models is presented.

Suggested Citation

  • Jewgeni H. Dshalalow, 1997. "On the level crossing of multi-dimensional delayed renewal processes," International Journal of Stochastic Analysis, Hindawi, vol. 10, pages 1-7, January.
    • Handle: RePEc:hin:jnijsa:707613
    DOI: 10.1155/S1048953397000415
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    Cited by:

    1. Jewgeni H. Dshalalow & Ryan T. White, 2021. "Current Trends in Random Walks on Random Lattices," Mathematics, MDPI, vol. 9(10), pages 1-38, May.
    2. Jewgeni H. Dshalalow & Hend Aljahani, 2023. "Discrete and Continuous Operational Calculus in N-Critical Shocks Reliability Systems with Aging under Delayed Information," Mathematics, MDPI, vol. 11(16), pages 1-27, August.
    3. Jewgeni H. Dshalalow & Ryan T. White, 2022. "Fluctuation Analysis of a Soft-Extreme Shock Reliability Model," Mathematics, MDPI, vol. 10(18), pages 1-33, September.
    4. Jewgeni H. Dshalalow & Ahmed Merie & Ryan T. White, 2020. "Fluctuation Analysis in Parallel Queues with Hysteretic Control," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 295-327, March.

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