Set-valued Brownian motion

Brownian motions, martingales, and Wiener processes are introduced and studied for set valued functions taking values in the subfamily of compact convex subsets of arbitrary Banach spaces X . The present paper is an application of the paper (Labuschagne et al. in Quaest Math 30(3):285–308, 2007 ) in which an embedding result is obtained which considers also the ordered structure of the family of compact convex subsets of a Banach space X and of Grobler and Labuschagne (J Math Anal Appl 423(1):797–819, 2015 ; J Math Anal Appl 423(1):820–833, 2015 ) in which these processes are considered in f-algebras. Moreover, in the space of continuous functions defined on a Stonian space, a direct Levy’s result follows.