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2 results

  • Collision probabilities for convex sets

  • Wolfgang Weil
  • Journal:
    Journal of Applied Probability / Volume 26 / Issue 3 / September 1989
    Published online by Cambridge University Press:
    14 July 2016, pp. 649-654
    Print publication:
    September 1989

  • Let K, L ⊂ En be non-empty, closed, convex sets, K bounded, and suppose boundary sets αof K and ß of L are painted. If K undergoes a random motion such that K and L touch, the probability for a paint-to-paint contact is expressed by curvature measures of K and L. This generalizes and simplifies previous work of Molter (1986) on infinite cylinders L touching a convex body K.

  • Densities for stationary random sets and point processes

  • Wolfgang Weil, John A. Wieacker
  • Journal:
    Advances in Applied Probability / Volume 16 / Issue 2 / June 1984
    Published online by Cambridge University Press:
    01 July 2016, pp. 324-346
    Print publication:
    June 1984

  • For certain stationary random sets X, densities Dφ (X) of additive functionals φ are defined and formulas for are derived when K is a compact convex set in . In particular, for the quermassintegrals and motioninvariant X, these formulas are in analogy with classical integral geometric formulas. The case where X is the union set of a Poisson process Y of convex particles is considered separately. Here, formulas involving the intensity measure of Y are obtained.