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1 results

  • Weak convergence and first passage times

  • Allan Gut
  • Journal:
    Journal of Applied Probability / Volume 12 / Issue 2 / June 1975
    Published online by Cambridge University Press:
    14 July 2016, pp. 324-332
    Print publication:
    June 1975

  • Let Sn, n = 1, 2, ‥, denote the partial sums of i.i.d. random variables with the common distribution function F and positive, finite mean. Let N(c) = min [k; Sk > c‥kp], c ≥ 0, 0 ≤ p < 1. Under the assumption that F belongs to the domain of attraction of a stable law with index α, 1 < α ≤ 2, functional central limit theorems for the first passage time process N(nt), 0 ≤ t ≤ 1, when n → ∞, are derived in the function space D[0,1].