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- W2127817383 abstract "In this paper we study the a} (p. 27 of [6]). It has been shown e.g. in [1] tha t this ordering may be equivalently defined by taking expectations of 'increasing product functions' g = Ylk=i 9ki 9k '• R —» R >o nondecreasing. In our study we restrict to lattice statespaces S C IL . On S we introduce a class T of nonnegative functions that contains the increasing product functions. In one dimension these functions are nondecreasing, in two dimensions nondecreasing and supermodular. Taking expectations we get the stochastic ordering < A ' again. The use of the T functions in stead of the increasing product functions has a benefit for obtaining stochastic ordering relations of Markov chains. A classical approach to derive ordering relations of Markov chains is based on monotonicity and comparability of the matrices of transition probabilities. These concepts may be defined by using a given stochastic ordering between probability measures e.g. <K or by using a class of functions on S e.g. the increasing product functions, or T -. It is well known that these two approaches are equivalent if the class of defining functions satisfies a certain closeness property (cf. [6]). We shall show that T does admit this property, but the increasing product functions do not. Moreover we shall prove that if the transition matrices of two Markov chains have the monotonicity and comparability properties and if the initial distributions are stochastically ordered (in <K), then all multidimensional marginal distributions of the chains are ordered as well. Finally we apply these concepts to open Jackson networks of queues for deriving (stochastic) comparison results in such networks." @default.
- W2127817383 created "2016-06-24" @default.
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- W2127817383 date "1993-01-01" @default.
- W2127817383 modified "2023-09-26" @default.
- W2127817383 title "On a stochastic ordering for random vectors and multidimensional Markov chains" @default.
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