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1 results

  • Interparticle dependence in a linear death process subjected to a random environment

  • Claude Lefèvre, György Michaletzky
  • Journal:
    Journal of Applied Probability / Volume 27 / Issue 3 / September 1990
    Published online by Cambridge University Press:
    14 July 2016, pp. 491-498
    Print publication:
    September 1990

  • Recently, Ball and Donnelly (1987) investigated the nature of the interparticle dependence in a death process with non-linear rates. In this note, after some remarks on their result, a similar problem is examined for a linear death process where the death rate per particle is a monotone function of the current state of a random environment. It is proved that if the exterior process involved is a homogeneous birth-and-death process valued in ℕ, then the survival times of any subset of particles are positively upper orthant dependent. A simple example shows that this property is not valid for general exterior processes.