Summary
The note concerns the structure of the Brownian excursion filtration (ε x, x∈R). This filtration, indexed by the space variable, has infinite martingale dimension. We show how it can be characterised by the martingale properties of the reflecting Brownian local time.
References
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McGill, P. A martingale characterisation of the Brownian excursion compensator. Probab. Th. Rel. Fields 71, 117–128 (1986). https://doi.org/10.1007/BF00366275
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DOI: https://doi.org/10.1007/BF00366275
Keywords
- Filtration
- Stochastic Process
- Probability Theory
- Local Time
- Mathematical Biology