Lévy's Brownian motion as a set-indexed process and a related central limit theorem
A representation of Lévy's Brownian motion with multi-dimensional time is given as a set-indexed process with independent increments. This construction yields a unified approach of Lévy's Brownian motion and the Brownian sheet, where a particular family of spheres plays the same basic role for Lévy's Brownian motion as the family of rectangles plays for the Brownian sheet. Some related limit theorems are proved for a natural family of set-indexed empirical processes.
Brownian motion with multi-dimensional time
set-indexed process with independent increments
scientific article; zbMATH DE number 3938123
scientific article