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1 results

  • Boundary crossing for moving sums

  • J. Glaz, B. Johnson
  • Journal:
    Journal of Applied Probability / Volume 25 / Issue 1 / March 1988
    Published online by Cambridge University Press:
    14 July 2016, pp. 81-88
    Print publication:
    March 1988

  • Let Xi, i ≧ 1, be a sequence of independent N(0, 1) random variables and Sj,m = Xj + · ·· + Xj+m–1, the jth moving sum. Let τ m = inf{j ≧ 1 : Sj,m > a} + m – 1, the boundary crossing time. Approximation in the spirit of Glaz and Johnson (1984), (1986) and Samuel-Cahn (1983) are given for Pr(τm > n), E(τ m), and σ (τ m),the standard deviation of τm.