Simulation of Stochastic Volterra Equations Driven by Space–Time Lévy Noise

Bohan Chen (), Carsten Chong () and Claudia Klüppelberg ()
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Bohan Chen: Technische Universität München
Carsten Chong: Technische Universität München
Claudia Klüppelberg: Technische Universität München

A chapter in The Fascination of Probability, Statistics and their Applications, 2016, pp 209-229 from Springer

Abstract: Abstract 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 $$L^p$$ 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.

Keywords: Simulation of SPDEs; Simulation of stochastic Volterra equations; Space–time Lévy noise; Stochastic heat equation; Stochastic partial differential equation (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-25826-3_10

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DOI: 10.1007/978-3-319-25826-3_10

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