From reflected Lévy processes to stochastically monotone Markov processes via generalized inverses and supermodularity

Abstract It was recently proven that the correlation function of stationary version a reflected Lévy process is nonnegative, nonincreasing, and convex. In another branch literature it established mean value starting from zero nondecreasing concave. present paper shown, by putting them in common framework, these results extend to substantially more general settings. Indeed, instead processes, we consider class stochastically monotone Markov processes. this setup show monotonicity associated with supermodular two coordinates our process, which above-mentioned convexity/concavity directly follow, but now for processes considered rather than just addition, various transient case (when not stationarity) are provided. The conditions imposed natural, they satisfied frequently used Markovian models, as illustrated series examples.