Erschienen in:

1987 | OriginalPaper | Buchkapitel

Skorokhod Topology and Convergence of Processes

verfasst von : Jean Jacod, Albert N. Shiryaev

Erschienen in: Limit Theorems for Stochastic Processes

Verlag: Springer Berlin Heidelberg

Enthalten in: Professional Book Archive

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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 (ℝd) of all càdlàg functions: ℝ₊→ ℝd 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).

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