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Parametric stochastic convexity and concavity of stochastic processes


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  • Moshe Shaked
  • J. Shanthikumar
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    Article provided by Springer in its journal Annals of the Institute of Statistical Mathematics.

    Volume (Year): 42 (1990)
    Issue (Month): 3 (September)
    Pages: 509-531

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    Handle: RePEc:spr:aistmt:v:42:y:1990:i:3:p:509-531

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    Keywords: Sample path convexity and concavity; Markov processes; directional convexity and concavity; single stage queues; supermodular and submodular functions; L-superadditive functions; reliability theory; branching processes; shock models; total positivity;


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    1. J. George Shanthikumar & David D. Yao, 1987. "Optimal Server Allocation in a System of Multi-Server Stations," Management Science, INFORMS, vol. 33(9), pages 1173-1180, September.
    2. L. Rüschendorf, 1983. "Solution of a statistical optimization problem by rearrangement methods," Metrika, Springer, vol. 30(1), pages 55-61, December.
    3. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
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    Cited by:
    1. Laureano Escudero & Eva-María Ortega, 2009. "How retention levels influence the variability of the total risk under reinsurance," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 17(1), pages 139-157, July.
    2. Escudero, Laureano F. & Ortega, Eva-María, 2008. "Actuarial comparisons for aggregate claims with randomly right-truncated claims," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 255-262, October.
    3. Xie, Hongmei & Hu, Taizhong, 2010. "Some new results on multivariate dispersive ordering of generalized order statistics," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 964-970, April.
    4. Arlotto, Alessandro & Scarsini, Marco, 2009. "Hessian orders and multinormal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2324-2330, November.
    5. Fabrizio Durante, 2009. "Construction of non-exchangeable bivariate distribution functions," Statistical Papers, Springer, vol. 50(2), pages 383-391, March.
    6. Fco. Javier Martinez de Albeniz Salas & Carlos Rafels Pallarola, 2002. "A Note on Shapleys Convex Measure Games," Working Papers in Economics 91, Universitat de Barcelona. Espai de Recerca en Economia.


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