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On the first passage times for Markov processes with monotone convex transition kernels

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  • Li, Haijun
  • Shaked, Moshe

Abstract

In this paper we study the first passage time for a damage process to exceed a given threshold or for the maximal increment of this process to pass a certain critical value. Conditions under which this first passage time possesses the NBU, the IFRA or the IFR properties are studied. An application to pure jump shock models is also discussed.

Suggested Citation

  • Li, Haijun & Shaked, Moshe, 1995. "On the first passage times for Markov processes with monotone convex transition kernels," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 205-216, August.
    • Handle: RePEc:eee:spapps:v:58:y:1995:i:2:p:205-216
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    References listed on IDEAS

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    1. Moshe Shaked & J. George Shanthikumar, 1987. "IFRA Properties of Some Markov Jump Processes with General State Space," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 562-568, August.
    2. Shaked, Moshe & Shanthikumar, J. George, 1987. "Temporal stochastic convexity and concavity," Stochastic Processes and their Applications, Elsevier, vol. 27, pages 1-20.
    3. Haijun Li & Moshe Shaked, 1994. "Stochastic Convexity and Concavity of Markov Processes," Mathematics of Operations Research, INFORMS, vol. 19(2), pages 477-493, May.
    4. Albert W. Marshall & Moshe Shaked, 1986. "NBU Processes with General State Space," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 95-109, February.
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    Cited by:

    1. L. Sacerdote & C. E. Smith, 2004. "Almost Sure Comparisons for First Passage Times of Diffusion Processes through Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 6(3), pages 323-341, September.
    2. Gut, Allan & Hüsler, Jürg, 2005. "Realistic variation of shock models," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 187-204, September.

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