Spectral approximation of a new class of stochastic fractional evolution equations
It provides a numerical approximation method for a recently proposed space-time extension of the SPDE-method in spatial statistics.
The paper introduces and analyzes a numerical method for a new class of fractional parabolic stochastic evolution equations, proving strong error bounds and verifying results with numerical experiments.
A method for numerical approximation of a new class of fractional parabolic stochastic evolution equations is introduced and analysed. This class of equations has recently been proposed as a space-time extension of the SPDE-method in spatial statistics. A truncation of the spectral basis function expansion is used to discretise in space, and then a quadrature is used to approximate the temporal evolution of each basis coefficient. Strong error bounds are proved both for the spectral and temporal approximations. The method is tested and the results are verified by several numerical experiments.