# Assume that the processes in Lemma 5.7 or in Lemma 5.8 are only almost surely right continuous,

## Question:

Assume that the processes in Lemma 5.7 or in Lemma 5.8 are only "almost surely right continuous", resp. "almost surely continuous". Identify all steps in the proofs where this becomes relevant and show that the assertions remain valid if the filtrations \(\mathscr{F}_{t}^{X}\) and \(\mathscr{F}_{t+}^{X}\) are completed, so that they contain all subsets of measurable null sets.

Data From Lemma 5.7

Data From Lemma 5.8

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**Related Book For**

## Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook

**ISBN:** 9783110741254

3rd Edition

**Authors:** René L. Schilling, Björn Böttcher