FWF Project No. P17139-N04

Cubature on Wiener Space


Principle Investigators: PreDoc: Funding period: May 2004 - April 2007



Scientific aims

Our aim in this research proposal is to point out several open problems for future research starting from the seminal work of T. Lyons and N. Victoir ('Cubature Formulas on Wiener Space', Proceedings of the Royal Society A, to appear). There are two main focusses: on the one hand we want to relate cubature formulas on Wiener space to the literature on parabolic initial value problems with sum of the squares generators, i.e. understand how the cubature formulas of T. Lyons and N. Victoir can be characterized by other points of view. On the other hand we are interested to compare the methodology of cubature formulas with respect to standard numerical methods for solving parabolic partial differential equations. We strongly believe that these two aims will be fruitful for each other and enable us to obtain a more complete picture for the analysis of parabolic initial value problems on geometric or analytic objects.