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2 results

  • A note on cumulative shock models

  • Kevin K. Anderson
  • Journal:
    Journal of Applied Probability / Volume 25 / Issue 1 / March 1988
    Published online by Cambridge University Press:
    14 July 2016, pp. 220-223
    Print publication:
    March 1988

  • A shock model in which the time intervals between shocks are in the domain of attraction of a stable law of order less than 1 or relatively stable is considered. Weak limit theorems are established for the cumulative magnitude of the shocks and the first time the cumulative magnitude exceeds z without any assumption on the dependence between the intershock interval and shock magnitude.

  • A limit theorem for semi-Markov processes

  • Domokos Szász
  • Journal:
    Journal of Applied Probability / Volume 11 / Issue 3 / September 1974
    Published online by Cambridge University Press:
    14 July 2016, pp. 521-528
    Print publication:
    September 1974

  • A limit theorem is proved for semi-Markov processes, which depend on a small parameter, tending to 0, in the case when the processes have an absorbing state and some asymptotically non-essential states and one asymptotically essential state. The application of the theorem is illustrated by an example from reliability theory.