Cubature on Wiener space in infinite dimension

Abstract

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 Lévy processes of finite type, here the results seem to be new even in finite dimension. Several numerical examples are added.

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

References in corpus (2)

• Existence of Lévy term structure models
• Hypoellipticity in infinite dimensions and an application in interest rate theory

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