Summary
Given a Brownian motionB, we consider the filtration (ℰ x xεR ), where ℰ x is defined as the σ-field generated by the excursions ofB belowx. In this paper we prove a conjecture of Walsh which says that all ε-martingales are continuous.
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Rogers, L.C.G. Continuity of martingales in the Brownian excursion filtration. Probab. Th. Rel. Fields 76, 291–298 (1987). https://doi.org/10.1007/BF01297486
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DOI: https://doi.org/10.1007/BF01297486
Keywords
- Filtration
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Brownian Excursion