Parametric stochastic convexity and concavity of stochastic processes (Q803654)

The present paper is a continuation of earlier publications of the authors [Stochastic Processes Appl. 27, No.1, 1-20 (1987; Zbl 0628.60095), Adv. Appl. Probab. 20, No.2, 427-446 (1988; Zbl 0656.60047) and ibid. 22, No.1, 160-177 (1990; Zbl 0697.60023)]. Here the notion of stochastic directional convexity (resp. concavity) together with appropriate assumptions is used to derive for a discrete time Markov process \(\{X_ n(\theta),\quad n=0,1,2,...\}\) with parameter \(\theta\) stochastic monotonicity and covexity of \(\{X_ n(\theta),\quad \theta \in \Theta \}\) for any n. The authors give applications of their main results in the fields of queueing systems, reliability theory and branching processes.