Completeness for a Brownian motion with polygonal stopping boundaries

B. Yakir, P. Huang, W. J. Hall

Research output: Contribution to journalArticlepeer-review


Consider a Brownian motion X(t) with drift θ ∈ J, a real interval, and a polygonal stopping boundary with hitting time T, assumed finite a.s. The boundary consists of upper and/or lower boundary functions that are piecewise-linear and continuous, and possibly a final vertical boundary. The statistic S ≡ (T, X(T)) is known to be sufficient for the past history of the process, for θ ∈ J. We show that the family (in θ) of distributions of S is complete. Relevance to sequential analysis is briefly noted.
Original languageAmerican English
Pages (from-to)201-208
Number of pages8
JournalSequential Analysis
Issue number3
StatePublished - 2001


  • Sequential analysis
  • UMVUE of drift
  • Secondary analysis
  • Curved stopping boundaries


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