The equation for vibrations of a fixed string driven by a general stochastic measure
Iryna Bodnarchuk, В. М. Радченко · Theory of Probability and Mathematical Statistics · 2021
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.