A central limit theorem for D(A)-valued processes
Let D(A) be the space of set-indexed functions that are outer continuous with inner limits, a generalization of D[0,1]. This paper proves a central limit theorem (CLT) for triangular arrays of independent D(A)- valued random variables. The limit processes are not restricted to be Gaussian, but can be quite general infinitely divisible processes. This is an important result with a basic and essential sense for the functional limit theory. Applications of this CLT include construction of set-indexed Levy processes and a unified CLT for partial sum processes and generalized empirical processes. Results obtained by this way are new even for the D[0,1] case.
scientific article; zbMATH DE number 4001087
scientific article