Abstract: We study solutions to nonlinear stochastic differential systems driven by a multi-dimensional Wiener process. We will start with a gentle and broad survey of numerical methods for solving stochastic differential systems; this will be the first half of my talk.
In the second half, we will consider strong simulation using the Castell--Gaines method, which is based on the exponential Lie series. We will demonstrate that when there is no drift, and the diffusion vector fields do not commute, the exponential Lie series is usurped by the sinh-log series. In particular, the mean-square error associated with a numerical method based on the sinh-log series, is always smaller than the corresponding stochastic Taylor error, in fact to all orders. We utilize the underlying Hopf algebra structure of these series. We illustrate the benefits of the proposed series in numerical studies.
Here is a link to the slides of Malham’s talk
Location: room 611 of the Wiskunde building (campus De Uithof) Budapestlaan 6, Utrecht.
Date and time: Thursday, December 3, 2009 15:30-16:30. The lecture is preceded by coffee, tea, and cookies from 15.00 to 15.30 hour in the same room.
Schedule of the Utrecht math colloquium : Next term’s talks, This year's talks. Last year's talks. Guidelines for speakers.
Other math colloquia : TU Delft, Leiden, UvA Amsterdam, VU Amsterdam, Nijmegen.
Organisers : Gil Cavalcanti, Wilberd van der Kallen and Paul Zegeling