Skorhod metric on a finite time interval

The notion of Skorohod metric provides a very useful topology in a discontinuous curve spaces, which is often arising as a sample space in stochastic analysis. Understanding Skorohod metric is also an interesting process for an undergraduate student, as a concrete example of a metric space but not a normed space. This note below is written by an undergraduate student with plenty of original examples.

PDF: here

Reference: [Bil99] ([Patrick Billingsley 1999])

 

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Skorohod metric

PDF: here

Reference: [Bil99] ([Patrick Billingsley 1999])

Goal: RCLL space is the collection of all right continuous processes with left limit exists. In this below, we will give a definition of Skorohod metric on this space. More precisely, for a {t\in (0, \infty)}, we denote by {\mathbb D^{d}_{t}} the collection of RCLL processes on {[0, t]} taking values in {\mathbb R^{d}}. We also use {\mathbb D^{d}_{\infty}} to denote the collection of RCLL processes on {[0, \infty)}.

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