Set-valued Brownian motion

Brownian motions, martingales, and Wiener processes are introduced andstudied for set valued functions taking values in the subfamily of compact convexsubsets 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 embeddingresult 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 AnalAppl 423(1):797–819, 2015; J Math Anal Appl 423(1):820–833, 2015) in which theseprocesses are considered in f-algebras.Moreover, in the space of continuous functionsdefined on a Stonian space, a direct Levy’s result follows.