A Criterion for Weak Convergence in Vector Skorokhod Spaces

Abstract

The paper considers random processes with values in a vector Skorokhod space; i.e., in a product of a finite number of Skorokhod spaces. Our interest is focused on weak convergence of a sequence of such processes. Particularly, we present a criterion for weak convergence in vector Skorokhod spaces. The idea is based on an embedding of a vector Skorokhod space into a Skorokhod space. Also, an illustrative example of two empirical processes is attached.