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Teor. Veroyatnost. i Primenen., 2002, Volume 47, Issue 2, Pages 255–269 (Mi tvp3646)  

Discrete wave equations with random parameters and a discrete string with random masses

L. D. Pustyl'nikov

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

Abstract: The problem under consideration is a modern development of one of the oldest problems of mathematics and mechanics: investigating oscillations of a string, the mass of which is concentrated in a finite number of equidistant points for the case where the masses are realizations of a sequence of random variables. By studying the corresponding differential equation with random parameters, explicit asymptotic expressions are obtained for frequencies and amplitudes of random oscillations and their probabilistic characteristics for a finite string and in which the number of points tends to infinity. Central limit theorems are established for functions characterizing frequencies of oscillations.

Keywords: discrete string, random masses, discrete wave equation with random parameters, frequencies of oscillations, amplitudes of oscillations.

DOI: https://doi.org/10.4213/tvp3646

Full text: PDF file (1318 kB)

English version:
Theory of Probability and its Applications, 2003, 47:2, 257–268

Bibliographic databases:

Received: 01.04.1999

Citation: L. D. Pustyl'nikov, “Discrete wave equations with random parameters and a discrete string with random masses”, Teor. Veroyatnost. i Primenen., 47:2 (2002), 255–269; Theory Probab. Appl., 47:2 (2003), 257–268

Citation in format AMSBIB
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\jour Theory Probab. Appl.
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