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The axis crossings of a stationary Gaussian Markov process

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1 Author(s)

In a stationary Gaussian Markov process (or Ornstein-Uhlenbeck process) the expected number of axis crossings per unit time, the probability density of the lengths of axis-crossing intervals, and the probability of recurrence at zero level do not exist as ordinarily defined. In this paper new definitions are presented and some asymptotic formulas are derived. Certain renewal equations are approximately satisfied, thereby suggesting an asymptotic approach to independence of the lengths of successive axis-crossing intervals. Mention is made of an application to the filter-clip-filter problem.

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IRE Transactions on Information Theory  (Volume:7 ,  Issue: 3 )