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1 results

  • The spectral density of a Markov process

  • B. D. Craven
  • Journal:
    Journal of Applied Probability / Volume 10 / Issue 3 / September 1973
    Published online by Cambridge University Press:
    14 July 2016, pp. 520-527
    Print publication:
    September 1973

  • For a Markov process in discrete time, having finite covariances, both the transient behaviour and the correlation structure may be summed up in a single generating function, here called the key function. If the process is stationary, and the key function possesses a suitable analytic extension, then the process possesses a continuous spectral density, which can be calculated from the key function. A converse result, and some results for the non-stationary process, are also obtained. The calculation is discussed in more detail for the waiting-time process in the GI/G/1 queue.