Skorokhod Topology and Convergence of Processes

Abstract

In this chapter, we lay down the last cornerstone that is needed to derive functional limit theorems for processes. Namely, we consider the space D (ℝ^d) of all càdlàg functions: ℝ₊→ ℝ^d we need to provide this space with a topology, such that: (1) the space is Polish (so we can apply classical limsit theorems on Polish spaces); (2) the Borel σ-field is exactly the σ-field generated by all evaluation maps (because the “law” of a process is precisely a measure on this σ-field).