Fourier transform of general stochastic measures

Abstract

The Fourier transform is defined for general stochastic measures in R d . The inversion theorem for this transform is proved and a connection to the convergence of stochastic integrals is established. An example of applications of this result is considered for the convergence of solutions of the stochastic heat equation.

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

“…Also, in some cases the rate of convergence in (15) and (31) may be estimated. By (18) and (32), we need to estimate η δj andη δj respectively.…”

“…Papers [15,17] contain examples of applying Fourier series of stochastic measures to the convergence of solutions of the stochastic heat equation. A similar application of the Fourier transform is given in [18]. Continuous dependence of solutions of wave equation upon the data was studied in [1,2].…”