FoCM 2014 conference

Workshop C6 - Stochastic Computation

December 20, 15:00 ~ 15:30 - Room C11

Explicit numerical schemes for SDEs driven by Levy noise and for Stochastic Evolution Equations

Sotirios Sabanis

University of Edinburgh, UK   -

The idea of 'tamed' Euler schemes, which was pioneered by Hutzenthaler, Jentzen and Kloeden [1] and Sabanis [2], led to the development of a new generation of explicit numerical schemes

- for SDEs driven by Levy noise with superlinear coefficients and,

- for stochastic evolutions equations with super-linearly growing operators appearing in the drift.

Moreover, high order schemes (such as Milstein) are established (with optimal rates of convergence) by the natural extension of the aforementioned ideas. Theoretical results on this topic along with relevant simulation outputs will be presented during this talk.

[1] M. Hutzenthaler, A. Jentzen, P.E. Kloeden, Strong convergence of an explicit numerical method for SDEs with non-globally Lipschitz continuous coefficients. Ann. Appl. Probab. 22 (2012) 1611--1641.

[2] S. Sabanis, A note on tamed Euler approximations, Electron. Commun. Probab. 18 (2013), no. 47, 1–-10.

Joint work with Istvan Gyongy (University of Edinburgh), David Siska (University of Edinburgh), Chaman Kumar (University of Edinburgh) and Konstantinos Dareiotis (University of Edinburgh).

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