Cubature on Wiener space in infinite dimension

Details Cubature on Wiener space in infinite dimension Cubature on Wiener space in infinite dimension

2007-12-21

arxiv.org/abs/0712.3763v2

Mathematics

Probability

revised version, accepted for publication in Proceedings Roy. Soc. A

Scientific paper

10.1098/rspa.2008.0013

We prove a stochastic Taylor expansion for SPDEs and apply this result to obtain cubature methods, i. e. high order weak approximation schemes for SPDEs, in the spirit of T. Lyons and N. Victoir. We can prove a high-order weak convergence for well-defined classes of test functions if the process starts at sufficiently regular initial values. We can also derive analogous results in the presence of L\'evy processes of finite type, here the results seem to be new even in finite dimension. Several numerical examples are added.

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