Sharp convergence rates of time discretization for stochastic time-fractional PDEs subject to additive space-time white noise

Abstract

The stochastic time-fractional equation ∂ t Ψ - Δ∂ t 1-α Ψ = f + W˙ with space-time white noise W˙ is discretized in time by a backward-Euler convolution quadrature for which the sharp-order error estimate [Formula] is established for α ∈ (0, 2/d), where d denotes the spatial dimension, Ψ n the approximate solution at the nth time step, and E the expectation operator. In particular, the result indicates sharp convergence rates of numerical solutions for both stochastic subdiffusion and diffusion-wave problems in one spatial dimension. Numerical examples are presented to illustrate the theoretical analysis. [Formula not complete, refer to publisher pdf]