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Mean Residual Life Processes and Associated Submartingales

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  • Antoine-Marie Bogso

    (University of Yaounde I)

Abstract

We use an argument of Madan and Yor to construct associated submartingales to a class of two-parameter processes that are ordered by increasing convex dominance. This class includes processes whose integrated survival functions are multivariate totally positive of order 2 ($$\hbox {MTP}_2$$MTP2). We prove that the integrated survival function of an integrable two-parameter process is $$\hbox {MTP}_2$$MTP2 if and only if it is totally positive of order 2 ($$\hbox {TP}_2$$TP2) in each pair of arguments when the remaining argument is fixed. This result cannot be deduced from known results since there are several two-parameter processes whose integrated survival functions do not have interval support. Since the $$\hbox {MTP}_2$$MTP2 property is closed under several transformations, it allows us to exhibit many other processes having the same total positivity property.

Suggested Citation

  • Antoine-Marie Bogso, 2020. "Mean Residual Life Processes and Associated Submartingales," Journal of Theoretical Probability, Springer, vol. 33(1), pages 36-64, March.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:1:d:10.1007_s10959-018-0865-6
    DOI: 10.1007/s10959-018-0865-6
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    References listed on IDEAS

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    1. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities II. Multivariate reverse rule distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 499-516, December.
    2. 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.
    3. Bogso, Antoine Marie, 2015. "MRL order, log-concavity and an application to peacocks," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1282-1306.
    4. Lim, Adrian P.C. & Yen, Ju-Yi & Yor, Marc, 2013. "Some examples of Skorokhod embeddings obtained from the Azéma–Yor algorithm," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 329-346.
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