Simulation of Stochastic Volterra Equations Driven by Space–Time Lévy Noise
In this paper we investigate two numerical schemes for the simulation of stochastic Volterra equations driven by space–time Lévy noise of pure-jump type. The first one is based on truncating the small jumps of the noise, while the second one relies on series representation techniques for infinitely divisible random variables. Under reasonable assumptions, we prove for both methods \(L^p\)- and almost sure convergence of the approximations to the true solution of the Volterra equation. We give explicit convergence rates in terms of the Volterra kernel and the characteristics of the noise. A simulation study visualizes the most important path properties of the investigated processes.
KeywordsSimulation of SPDEs Simulation of stochastic Volterra equations Space–time Lévy noise Stochastic heat equation Stochastic partial differential equation
We take pleasure in thanking Jean Jacod for his valuable advice on this subject. The second author acknowledges support from the Studienstiftung des deutschen Volkes and the graduate programme TopMath at Technische Universität München.
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