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In this paper we investigate two numerical schemes for the simulation ofstochastic Volterra equations driven by space--time L\'evy noise of pure-jumptype. The first one is based on truncating the small jumps of the noise, whilethe second one relies on series representation techniques for infinitelydivisible random variables. Under reasonable assumptions, we prove for bothmethods $L^p$- and almost sure convergence of the approximations to the truesolution of the Volterra equation. We give explicit convergence rates in termsof the Volterra kernel and the characteristics of the noise. A simulation studyvisualizes the most important path properties of the investigated processes.

Simulation of stochastic Volterra equations driven by space--time L\'evy noise