Stochastic Monotonicity

  • Julian Keilson
Part of the Applied Mathematical Sciences book series (AMS, volume 28)


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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Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Julian Keilson
    • 1
  1. 1.The University of RochesterRochesterUSA

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