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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1708.05858 |
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Table of Contents:
- We consider a filtration $\mathbb{G}$ obtained as enlargement of a filtration $\mathbb{F}$ by a filtration $\mathbb{H}$. We assume that all $\mathbb{F}$-local martingales are represented by a martingale $M$ and all $\mathbb{H}$-local martingales are represented by a martingale $N$. $M$ and $N$ are not necessarily quasi-left continuous processes and their jump times may overlap. We first analyze the contribution of the accessible jump times of $M$ and $N$ to the Jacod's dimension of the space of the $\mathcal{H}^1(\mathbb{G})$-martingales. Then we prove a new martingale representation theorem on $\mathbb{G}$.