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1 results

  • Distribution of the supremum of the two-parameter Yeh-Wiener process on the boundary

  • S. R. Paranjape, C. Park
  • Journal:
    Journal of Applied Probability / Volume 10 / Issue 4 / December 1973
    Published online by Cambridge University Press:
    14 July 2016, pp. 875-880
    Print publication:
    December 1973

  • Let D = [0, S] × [0, T] be a rectangle in E2 and X(s, t), (s, t)∈D, be a two parameter Yeh-Wiener process. This paper finds the probability distribution of the supremum of X(s, t) on the boundary of D by taking the limit of the probability distribution of the supremum of X(s, t) along certain paths as these paths approach the boundary of D. The probability distribution of the supremum of X(s, t) on the boundary of D gives a nice lower bound for the probability distribution of the supremum of X(s, t) on D, which is unknown.