Set-valued Brownian motion

Abstract

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 space $X$. The present paper is an application of one the paper of the second author in which an embedding result is obtained which considers also the ordered structure of $ck(X)$ and f-algebras.

15 pages, 1 figure

References in corpus (5)

• The Choquet integral with respect to fuzzy measures and applications
• Markov processes on Riesz spaces
• Henstock multivalued integrability in Banach lattices with respect to pointwise non atomic measures
• $L^p$ spaces in vector lattices and applications
• Comparison between some norm and order gauge integrals in Banach lattices

Cited by in corpus (3)

• A vector Girsanov result and its applications to conditional measures via the Birkhoff integrability
• A Girsanov Result through Birkhoff Integral
• A Girsanov result for the Pettis integral