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1 results

  • General solidarity theorems for semi-Markov processes

  • Choong K. Cheong, Jozef L. Teugels
  • Journal:
    Journal of Applied Probability / Volume 9 / Issue 4 / December 1972
    Published online by Cambridge University Press:
    14 July 2016, pp. 789-802
    Print publication:
    December 1972

  • Let {Zt, t ≧ 0} be an irreducible regular semi-Markov process with transition probabilities Pij (t). Let f(t) be non-negative and non-decreasing to infinity, and let λ ≧ 0. This paper identifies a large set of functions f(t) with the solidarity property that convergence of the integral ≧ eλtf(t)Pij(t) dt for a specific pair of states i and j implies convergence of the integral for all pairs of states. Similar results are derived for the Markov renewal functions Mij (t). Among others it is shown that f(t) can be taken regularly varying.