The Fluctuations of the Number and the Interval Length in the Level-Crossing Problem

Hiroshi SATO  Masami TANABE  Tadashi MIMAKI  

IEICE TRANSACTIONS (1976-1990)   Vol.E68   No.9   pp.586-593
Publication Date: 1985/09/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Stochastic Process

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The so-called level-crossing problem of a random process is concerned with the properties of a sequence of time points at which the random process crosses with a fixed level. In order to intuitively understand the various properties of the level-crossing problem, we employ the ransom excursion model as a simple mode of a random process, by which the level dependence of the fluctuation of the number of the crossing points is derived for Gaussian processes having modified lowpass spectra. The comparison of the derived result with exact calculation is satisfactory. Secondly, we estimate how the magnitude of the fluctuation of the number for a narrow bandpass Gaussian process is different from that of an independent point process. Finally we obtain expressions for variance of the lengths of the level-crossing intervals and other quantities for a narrow bandpass Gaussian process and we succeed in interpreting the experimentally obtained behavior of the above variance.