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First excess levels of vector processes

Author

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  • Jewgeni H. Dshalalow

Abstract

This paper analyzes the behavior of a point process marked by a two-dimensional renewal process with dependent components about some fixed (two-dimensional) level. The compound process evolves until one of its marks hits (i.e. reaches or exceeds) its associated level for the first time. The author targets a joint transformation of the first excess level, first passage time, and the index of the point process which labels the first passage time. The cases when both marks are either discrete or continuous or mixed are treated. For each of them, an explicit and compact formula is derived. Various applications to stochastic models are discussed.

Suggested Citation

  • Jewgeni H. Dshalalow, 1994. "First excess levels of vector processes," International Journal of Stochastic Analysis, Hindawi, vol. 7, pages 1-8, January.
    • Handle: RePEc:hin:jnijsa:762639
    DOI: 10.1155/S1048953394000365
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    Cited by:

    1. Song-Kyoo (Amang) Kim, 2022. "Shifted Brownian Fluctuation Game," Mathematics, MDPI, vol. 10(10), pages 1-12, May.
    2. Jewgeni H. Dshalalow & Ryan T. White, 2021. "Current Trends in Random Walks on Random Lattices," Mathematics, MDPI, vol. 9(10), pages 1-38, May.
    3. Song-Kyoo (Amang) Kim, 2022. "Versatile Stochastic Two-Sided Platform Models," Mathematics, MDPI, vol. 11(1), pages 1-15, December.

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