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On The Error Estimate for Cubature on Wiener Space

Published online by Cambridge University Press:  29 November 2013

Thomas Cass
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK, (c.litterer@imperial.ac.uk)
Christian Litterer
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK, (c.litterer@imperial.ac.uk)

Abstract

It was pointed out by Crisan and Ghazali that the error estimate for the cubature on Wiener space algorithm developed by Lyons and Victoir requires an additional assumption on the drift. In this paper we demonstrate that it is straightforward to adopt the analysis of Kusuoka to obtain a general estimate without an additional assumptions on the drift. In the process we slightly sharpen the bounds derived by Kusuoka.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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