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

Hiroshi SATO; Masami TANABE; Tadashi MIMAKI

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

Hiroshi SATO, Masami TANABE, Tadashi MIMAKI

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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.

Publication: IEICE TRANSACTIONS on transactions Vol.E68-E No.9 pp.586-593

Publication Date: 1985/09/25

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Type of Manuscript: PAPER

Category: Stochastic Process

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Hiroshi SATO
Masami TANABE
Tadashi MIMAKI

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Hiroshi SATO, Masami TANABE, Tadashi MIMAKI, "The Fluctuations of the Number and the Interval Length in the Level-Crossing Problem" in IEICE TRANSACTIONS on transactions, vol. E68-E, no. 9, pp. 586-593, September 1985, doi: .
Abstract: 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.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e68-e_9_586/_p

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@ARTICLE{e68-e_9_586,
author={Hiroshi SATO, Masami TANABE, Tadashi MIMAKI, },
journal={IEICE TRANSACTIONS on transactions},
title={The Fluctuations of the Number and the Interval Length in the Level-Crossing Problem},
year={1985},
volume={E68-E},
number={9},
pages={586-593},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={September},}

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TY - JOUR
TI - The Fluctuations of the Number and the Interval Length in the Level-Crossing Problem
T2 - IEICE TRANSACTIONS on transactions
SP - 586
EP - 593
AU - Hiroshi SATO
AU - Masami TANABE
AU - Tadashi MIMAKI
PY - 1985
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E68-E
IS - 9
JA - IEICE TRANSACTIONS on transactions
Y1 - September 1985
AB - 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.
ER -