The space D(A) and weak convergence for set-indexed processes
A topology is introduced for the space D(A) of functions which are outer continuous with inner limits indexed by a family of Borel subsets of the d-dimensional unit cube. The space is a natural extension of D[0,1] as a range space of sample paths for processes indexed by a family of sets. Weak convergence of such processes is considered. The topology is similar in spirit to the \(M_ 2\) topology of Skorokhod for D[0,1] in that the distance between two functions is defined by the Hausdorff distance between their graphs. A central limit theorem for partial-sum processes indexed by a family of sets is established.
scientific article; zbMATH DE number 3938122