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Temporal stochastic convexity and concavity

Author

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  • Shaked, Moshe
  • Shanthikumar, J. George

Abstract

A discrete time stochastic process {Xn, N = 0, 1, 2, ...} is said to be temporally convex (concave) if E[theta](Xn) is a nondecreasing convex (concave) function of n whenever [theta] is a nondecreasing convex (concave) function. Similarly one can define temporal convexity and concavity for continuous time stochastic processes. In this paper we find conditions which imply that a given Markov process is temporally convex or concave. Some illustrative examples of stochastic temporal convexity and concavity in reliability theory, queueing theory, branching processes and record values are given. Finally an application of temporal stochastic concavity to a problem in computational probability is described.

Suggested Citation

  • Shaked, Moshe & Shanthikumar, J. George, 1987. "Temporal stochastic convexity and concavity," Stochastic Processes and their Applications, Elsevier, vol. 27, pages 1-20.
    • Handle: RePEc:eee:spapps:v:27:y:1987:i::p:1-20
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    Citations

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    Cited by:

    1. Moshe Shaked & J. Shanthikumar, 1990. "Parametric stochastic convexity and concavity of stochastic processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(3), pages 509-531, September.
    2. 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.
    3. Denuit, Michel & Mesfioui, Mhamed, 2013. "Multivariate higher-degree stochastic increasing convexity," LIDAM Discussion Papers ISBA 2013016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Ludolf E. Meester & J. George Shanthikumar, 1999. "Stochastic Convexity on General Space," Mathematics of Operations Research, INFORMS, vol. 24(2), pages 472-494, May.

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