The equation for vibrations of a fixed string driven by a general stochastic measure

Bodnarchuk, I.; Radchenko, V.

doi:10.1090/tpms/1108

The equation for vibrations of a fixed string driven by a general stochastic measure

Authors: I. M. Bodnarchuk and V. M. Radchenko
Translated by: N. N. Semenov
Journal: Theor. Probability and Math. Statist. 101 (2020), 1-11
MSC (2020): Primary 60H15; Secondary 60G17, 60G57
DOI: https://doi.org/10.1090/tpms/1108
Published electronically: January 5, 2021
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Abstract: The existence of a mild solution of the equation for vibrations of a homogeneous string with fixed ends driven by a general stochastic measure is studied in the following three cases: the stochastic measure depends on (1) the time variable, (2) the spatial variable, (3) the set of all variables. The averaging principle is considered and the rate of convergence to a solution of the averaged equation is obtained.

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