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 , Veinott , and Daley , and discussed further by O’Brien , Kirstein , Keilson and Kester , , and Whitt and Sonderman . 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.
Unable to display preview. Download preview PDF.