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On The Error Estimate for Cubature on Wiener Space

Published online by Cambridge University Press:  29 November 2013

Thomas Cass  and
Christian Litterer
Thomas Cass
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK, ([email protected])
Christian Litterer
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK, ([email protected])
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Abstract

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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.

Keywords

cubaturestochastic differential equationssignature 2010Primary 65C30
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 2 , June 2014 , pp. 377 - 391
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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