Spat1otemporal convexity of stochastic processes and applications

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)1-16
Journal / PublicationProbability in the Engineering and Informational Sciences
Volume6
Issue number1
Publication statusPublished - Jan 1992
Externally publishedYes

Abstract

A stochastic process {X1(s)} is viewed as a collection of random variables parameterized by time (t) and the initial state (s). {X∣(s)} is termed spatiotemporally increasing and convex if, in a sample-path sense, it is increasing in s and t and satisfies a directional convexity property, which implies that it is increasing and convex in s and in t (individually) and is supermodular in (5, t). Simple sufficient conditions are established for a uniformizable Markov process to be spatiotemporally increasing and convex. The results are applied to study the convex orderings in Gl/M(n)/1 and M(n)/G/1 queues and to solve the optimal allocation of a joint setup among several production facilities. For a counting process that possesses a stochastic intensity, we show that its spatiotemporal behavior can be characterized by its conditional intensity via a birth process. © 1992, Cambridge University Press. All right reserved.