Abstract
A Markov process X(t) is said to be monotone if P[X(t) > x | X(0) = y] increases with y for every fixed x. The monotonicity of operators governing processes was introduced by Kalmykov [20], Veinott [64], and Daley [10], and discussed further by O’Brien [56], Kirstein [49], Keilson and Kester [36], [37], and Whitt and Sonderman [65]. The property is simple and widespread, and lends itself to a variety of structural insights. In particular, it is basic to many interesting inequalities in reliability theory.
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© 1979 Springer-Verlag New York Inc.
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Keilson, J. (1979). Stochastic Monotonicity. In: Keilson, J. (eds) Markov Chain Models — Rarity and Exponentiality. Applied Mathematical Sciences, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6200-8_10
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DOI: https://doi.org/10.1007/978-1-4612-6200-8_10
Publisher Name: Springer, New York, NY
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