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A note on first passage times in birth and death and nonnegative diffusion processes

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  • Cyrus Derman
  • Sheldon M. Ross
  • Zvi Schechner

Abstract

Consider a birth and death process starting in state 0. Keilson has shown by analytical arguments that the time of first passage into state n has an increasing failure rate (IFR) distribution. We present a probabilistic proof for this. In addition, our proof shows that for a nonnegative diffusion process, the first passage time from state 0 to any state x is IFR.

Suggested Citation

  • Cyrus Derman & Sheldon M. Ross & Zvi Schechner, 1983. "A note on first passage times in birth and death and nonnegative diffusion processes," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 30(2), pages 283-285, June.
    • Handle: RePEc:wly:navlog:v:30:y:1983:i:2:p:283-285
    DOI: 10.1002/nav.3800300209
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    Cited by:

    1. Michael Katehakis & Ingram Olkin & Sheldon Ross & Jian Yang, 2013. "On the life and work of Cyrus Derman," Annals of Operations Research, Springer, vol. 208(1), pages 5-26, September.

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