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.

Keywords

• Random processes
• Skorokhod spaces
• Weak convergence of measures
• Tightness of measures