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On cumulative jump random variables

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  • Michael Tortorella

Abstract

Stochastic models for phenomena that can exhibit sudden changes involve the use of processes whose sample functions may have discontinuities. This paper provides some tools for working with such processes. We develop a sample path formula for the cumulative jump height over a given time interval. From this formula an expression for the expected value of the cumulative jump random variable is developed under reasonable conditions. The results are applied to finding the expected number of failures in the separate maintenance model over a stated time interval and to the expected number of occurrences of a regenerative event over a stated time interval. Copyright Springer Science+Business Media New York 2013

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  • Michael Tortorella, 2013. "On cumulative jump random variables," Annals of Operations Research, Springer, vol. 206(1), pages 485-500, July.
    • Handle: RePEc:spr:annopr:v:206:y:2013:i:1:p:485-500:10.1007/s10479-013-1319-2
    DOI: 10.1007/s10479-013-1319-2
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    References listed on IDEAS

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    1. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 21(6), pages 2535-2563, November.
    2. M. Kijima & T. Suzuki, 2001. "A jump-diffusion model for pricing corporate debt securities in a complex capital structure," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 611-620.
    3. Michael Tortorella, 2005. "Numerical Solutions of Renewal-Type Integral Equations," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 66-74, February.
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