A central limit theorem for D( A)-valued processes

Abstract

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 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. Applications of the theorem include construction of set-indexed Lévy processes and a unified central limit theorem for partial sum processes and generalized empirical processes. Results obtained are new even for the D[0, 1] case.