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Intensity of Crossings of a Given Level by a Homogeneous Random Field

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Cybernetics and Systems Analysis Aims and scope

Abstract

The author defines the concept of the intensity of crossings of a given level by a homogeneous field as average number of points of level surface that hit the expanding space. It is shown that irrespective of the position of the center of expanding space, the problem of finding the intensity reduces to counting the level surfaces per unit volume. The author formulates the possibility of finding the number of level surfaces as a characteristic that depends on surface generating points. A differential equation is found that relates the intensities of points of local maxima and local minima with the desired intensity of level surfaces. The accuracy of the results is verified for the stationary Gaussian process. The results completely coincide with the expression first found by Rice.

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Authors and Affiliations

  1. National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

    D. V. Yevgrafov

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  1. D. V. Yevgrafov
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Correspondence to D. V. Yevgrafov.

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Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2017, pp. 151–159.

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Yevgrafov, D.V. Intensity of Crossings of a Given Level by a Homogeneous Random Field. Cybern Syst Anal 53, 785–792 (2017). https://doi.org/10.1007/s10559-017-9981-z

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  • DOI: https://doi.org/10.1007/s10559-017-9981-z

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