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1 results

  • Stochastic barriers for the Wiener process

  • C. Park, J. A. Beekman
  • Journal:
    Journal of Applied Probability / Volume 20 / Issue 2 / June 1983
    Published online by Cambridge University Press:
    14 July 2016, pp. 338-348
    Print publication:
    June 1983

  • Let {W(t), 0 ≦ t < ∞} be the standard Wiener process. The probabilities of the type P[sup0≦t ≦ TW(t) − f(t) ≧ 0] have been extensively studied when f(t) is a deterministic function. This paper discusses the probabilities of the type P{sup0≦t ≦ TW(t) − [f(t) + X(t)] ≧ 0} when X(t) is a stochastic process. By taking compound Poisson processes as X(t), the paper gives procedures for finding such probabilities.