Comparison of time-inhomogeneous Markov processes. (English) Zbl 1384.60063

Rüschendorf, Ludger; Schnurr, Alexander; Wolf, Victor

Adv. Appl. Probab. 48, No. 4, 1015-1044 (2016).

Summary: Comparison results are given for time-inhomogeneous Markov processes with respect to function classes with induced stochastic orderings. The main result states the comparison of two processes, provided that the comparability of their infinitesimal generators as well as an invariance property of one process is assumed. The corresponding proof is based on a representation result for the solutions of inhomogeneous evolution problems in Banach spaces, which extends previously known results from the literature. Based on this representation, an ordering result for Markov processes induced by bounded and unbounded function classes is established. We give various applications to time-inhomogeneous diffusions, to processes with independent increments, and to Lévy-driven diffusion processes.

MSC:

60E15	Inequalities; stochastic orderings
60J35	Transition functions, generators and resolvents
60J75	Jump processes (MSC2010)

Keywords:

stochastic ordering; Markov process; infinitesimal generator; processes with independent increments; evolution system