On the existence of modified equations for stochastic differential equations
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Tue, 26/01/2010 14:00 |
Dr Konstantinos Zyglakis (OCCAM (Oxford)) |
Computational Mathematics and Applications  |
3WS SR |
| In this talk we describe a general framework for deriving modified equations for stochastic differential equations with respect to weak convergence. We will start by quickly recapping of how to derive modified equations in the case of ODEs and describe how these ideas can be generalized in the case of SDEs. Results will be presented for first order methods such as the Euler-Maruyama and the Milstein method. In the case of linear SDEs, using the Gaussianity of the underlying solutions, we will derive a SDE that the numerical method solves exactly in the weak sense. Applications of modified equations in the numerical study of Langevin equations and in the calculation of effective diffusivities will also be discussed. | |||