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1 results

  • Further results on ASTA for general stationary processes and related problems

  • Masakiyo Miyazawa, Ronald W. Wolff
  • Journal:
    Journal of Applied Probability / Volume 27 / Issue 4 / December 1990
    Published online by Cambridge University Press:
    14 July 2016, pp. 792-804
    Print publication:
    December 1990

  • We consider the equivalence of state probabilities of a general stationary process at an arbitrary time and at embedded epochs of a given point process, which is called ASTA (Arrivals See Time Averages). By using an event-conditonal intensity, we give necessary and sufficient conditions for ASTA for a large class of state sets, which determines a state distribution. We do not need any additional assumptions except that the general process has left-hand limits at all points of time. Especially, for a stationary pure-jump process with a point process, ASTA is obtained for all state sets. As an application of those results, Anti-PASTA is obtained for a pure-jump Markov process and a certain class of GSMP (Generalized Semi-Markov Processes), where Anti-PASTA means that ASTA implies that the arrival process is Poisson.