Approximation of solutions of the stochastic wave equation by using the Fourier series

Abstract

A one-dimensional stochastic wave equation driven by a general stochastic measure is studied in this paper. The Fourier series expansion of stochastic measures is considered. It is proved that changing the integrator by the corresponding partial sums or by Fejèr sums we obtain the approximations of mild solution of the equation.

Averaging principle for a stochastic cable equation

“…In [2] the ergodic property of the solution to a fractional stochastic heat equation is established. Wave equations with general stochastic measures and α-stable distributions are investigated in the papers [5,7,8,24] and [20,29,19], respectively.…”