Order preserving and order reversing operators on the class of $L^0$-convex functions in complete random normed modules

Abstract: Based on both the fundamental theorem of affine geometry in regular $L^0$-modules and the recent progress in random convex analysis, this paper characterizes the stable fully order preserving and order reversing operators acting on the class of proper lower semicontinuous $L^0$-convex functions in complete random normed modules.