Geodesic
Discrete wave equations with random parameters and a discrete string with random masses
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 2, pp. 255-269

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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
Mots-clés : amplitudes of oscillations. 
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     author = {L. D. Pustyl'nikov},
     title = {Discrete wave equations with random parameters and a discrete string with random masses},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {255--269},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_2_a2/}
}
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L. D. Pustyl'nikov. Discrete wave equations with random parameters and a discrete string with random masses. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 2, pp. 255-269. http://geodesic.mathdoc.fr/item/TVP_2002_47_2_a2/