Remarks on the Convex Minorant of Brownian Motion

  • J. W. Pitman
Part of the Progress in Probability and Statistics book series (PRPR, volume 5)


Recently Groeneboom [1] studied the concave majorant process of a Brownian motion (Bt, t ≤ O). The purpose of this note is to take a fresh look at some of Groeneboom’s results in the context of path decompositions of Williams [7], and to give a simple new description of this concave majorant process.


Brownian Motion Time Inversion Poisson Point Process Independent Increment Bessel Process 
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Copyright information

© Birkhäuser, Boston, Inc. 1983

Authors and Affiliations

  • J. W. Pitman
    • 1
  1. 1.Department of StatisticsUniv. of California at BerkeleyBerkeleyUSA

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