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Elena ISSOGLIO (The University of Leeds) – “A numerical scheme for multidimensional SDEs with distributional drift “
November 5, 2018, 3:45 pm - 4:45 pm
1st Monday of each month
Time: 4:45 pm – 5:45 pm
Date: 05 th of November 2018
Place: Room 3105
Elena ISSOGLIO (The University of Leeds) – “A numerical scheme for multidimensional SDEs with distributional drift ”
Abstract : This talk focuses on a multidimensional SDE where the drift is an element of a fractional Sobolev space with negative order, hence a distribution. This SDE admits a unique weak solution in a suitable sense – this was proven in [Flandoli, Issoglio, Russo (2017)]. The aim here is to construct a numerical scheme to approximate this solution. One of the key problems is that the drift cannot be evaluated pointwise, hence we approximate it with suitable functions using Haar wavelets, and then apply (an extended version of) Euler-Maruyama scheme. We then show that the algorithm converges in law, and in the special 1-dimensional case we also get a rate of convergence (and in fact convergence in L^1).
This is based on a joint work with T. De Angelis and M. Germain.