Continuity of martingales in the Brownian excursion filtration (Q1087245)
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scientific article; zbMATH DE number 3988413
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Continuity of martingales in the Brownian excursion filtration |
scientific article; zbMATH DE number 3988413 |
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Continuity of martingales in the Brownian excursion filtration (English)
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1987
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Given a Brownian motion B, we consider the filtration (\({\mathcal E}_ x)_{x\in R}\), where \({\mathcal E}_ x\) is defined as the \(\sigma\)-field generated by the excursions of B below x. In this paper we prove a conjecture by J. B. Walsh which says that all \({\mathcal E}\)-martingales are continuous.
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excursion filtration
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Brownian motion
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