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.
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Müller-Gronbach, T., Ritter, K., Wagner, T. (2008). Optimal Pointwise Approximation of a Linear Stochastic Heat Equation with Additive Space-Time White Noise. In: Keller, A., Heinrich, S., Niederreiter, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74496-2_34
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DOI: https://doi.org/10.1007/978-3-540-74496-2_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74495-5
Online ISBN: 978-3-540-74496-2
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