  We extend a Discrete Time Random Walk (DTRW) numerical scheme to simulate the
anomalous diffusion of financial market orders in a simulated order book. Here
using random walks with Sibuya waiting times to include a time-dependent
stochastic forcing function with non-uniformly sampled times between order book
events in the setting of fractional diffusion. This models the fluid limit of
an order book by modelling the continuous arrival, cancellation and diffusion
of orders in the presence of information shocks. We study the impulse response
and stylised facts of orders undergoing anomalous diffusion for different
forcing functions and model parameters. Concretely, we demonstrate the price
impact for flash limit-orders and market orders and show how the numerical
method generate kinks in the price impact. We use cubic spline interpolation to
generate smoothed price impact curves. The work promotes the use of non-uniform
sampling in the presence of diffusive dynamics as the preferred simulation
method.
