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

In: Monte Carlo and Quasi-Monte Carlo Methods 2006

Author

Listed:
  • 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)

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.

Suggested Citation

  • Thomas Müller-Gronbach & Klaus Ritter & Tim Wagner, 2008. "Optimal Pointwise Approximation of a Linear Stochastic Heat Equation with Additive Space-Time White Noise," Springer Books, in: Alexander Keller & Stefan Heinrich & Harald Niederreiter (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2006, pages 577-589, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-74496-2_34
    DOI: 10.1007/978-3-540-74496-2_34
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