Temporal stochastic convexity and concavity

A discrete time stochastic process {Xn, N = 0, 1, 2, ...} is said to be temporally convex (concave) if E[theta](Xn) is a nondecreasing convex (concave) function of n whenever [theta] is a nondecreasing convex (concave) function. Similarly one can define temporal convexity and concavity for continuous time stochastic processes. In this paper we find conditions which imply that a given Markov process is temporally convex or concave. Some illustrative examples of stochastic temporal convexity and concavity in reliability theory, queueing theory, branching processes and record values are given. Finally an application of temporal stochastic concavity to a problem in computational probability is described.