The Cereteli-Davis Solution to the H1-Embedding Problem and an Optimal Embedding in Brownian Motion

  • Edwin Perkins
Part of the Progress in Probability and Statistics book series (PRPR, volume 12)


Necessary and sufficient conditions are found on a mean-zero probability, μ, for the existence of a stopping time, T, and a Brownian motion, B, such that BT has law μ and \( B_T^{*} \) is integrable. This result, due to Burgess Davis (the classical analogue was first solved by O. D. Cereteli), leads naturally to a stopping time, T, that stochastically minimizes both sups≤TBs and -infs≤TBs.


Brownian Motion Maximal Function Conjugate Function Optimal Embedding Filling Scheme 
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Copyright information

© Birkhäuser Boston, Inc. 1986

Authors and Affiliations

  • Edwin Perkins
    • 1
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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