Title: Hybrid simulation scheme for volatility modulated moving average fields,
Abstract: We develop a simulation scheme for a class of spatial stochastic processes
called volatility modulated moving averages. A characteristic feature of this
model is that the behaviour of the moving average kernel at zero governs the
roughness of realisations, whereas its behaviour away from zero determines the
global properties of the process, such as long range dependence. Our simulation
scheme takes this into account and approximates the moving average kernel by a
power function around zero and by a step function elsewhere. For this type of
approach the authors of [8], who considered an analogous model in one
dimension, coined the expression hybrid simulation scheme. We derive the
asymptotic mean square error of the simulation scheme and compare it in a
simulation study with several other simulation techniques and exemplify its
favourable performance in a simulation study.