Christian Bayer, Josef Teichmann
Published 2007-12-21, updated 2008-04-28Version 2
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.
Comments: revised version, accepted for publication in Proceedings Roy. Soc. A
High order weak approximation schemes for Lévy-driven SDEs
Decoupling on the Wiener space and applications to BSDEs
The Monge-Kantorovitch Problem and Monge-Ampere Equation on Wiener Space
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