Optimal Pointwise Approximation of a Linear Stochastic Heat Equation with Additive Space-Time White Noise

Thomas Müller-Gronbach (), Klaus Ritter () and Tim Wagner ()
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Thomas Müller-Gronbach: Fern Universität Hagen, Fakultät für Mathematik und Informatik
Klaus Ritter: Universität Darmstadt, Fachbereich Mathematik, Technische
Tim Wagner: Universität Darmstadt, Fachbereich Mathematik, Technische

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2006, 2008, pp 577-589 from Springer

Abstract: Summary We consider a linear stochastic heat equation on the spatial domain ]0, 1[ with additive space-time white noise, and we study approximation of the mild solution at a fixed time instance. We show that a drift-implicit Euler scheme with a non-equidistant time discretization achieves the order of convergence N -1/2, where N is the total number of evaluations of one-dimensional components of the driving Wiener process. This order is best possible and cannot be achieved with an equidistant time discretization.

Keywords: Brownian Motion; Mild Solution; Stochastic Evolution Equation; Stochastic Heat Equation; Implicit Euler Scheme (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-74496-2_34

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DOI: 10.1007/978-3-540-74496-2_34

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