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The spectral density of a Markov process

Published online by Cambridge University Press:  14 July 2016

B. D. Craven*
University of Melbourne


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.

Research Papers
Copyright © Applied Probability Trust 1973 

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