Mean Residual Life Processes and Associated Submartingales

Antoine-Marie Bogso ()
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Antoine-Marie Bogso: University of Yaounde I

Journal of Theoretical Probability, 2020, vol. 33, issue 1, 36-64

Abstract: 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.

Keywords: Cox–Hobson algorithm; Incomplete Markov processes; MRL ordering; Two-parameter submartingales; Total positivity; 60E15; 60G44; 60J25; 32F17 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-018-0865-6

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