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Continuity of martingales in the Brownian excursion filtration
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  • Published: September 1987

Continuity of martingales in the Brownian excursion filtration

  • L. C. G. Rogers1 

Probability Theory and Related Fields volume 76, pages 291–298 (1987)Cite this article

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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Authors and Affiliations

  1. Statistical Laboratory, 16 Mill Lane, CB2 1SB, Cambridge, UK

    L. C. G. Rogers

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  1. L. C. G. Rogers
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Cite this article

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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  • Received: 02 December 1986

  • Issue Date: September 1987

  • DOI: https://doi.org/10.1007/BF01297486

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Keywords

  • Filtration
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Brownian Excursion
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