title:
A deterministic algorithm based on discretized WagnerPlaten steps for quadrature of marginals of SDEs 
name:
Yaroslavtseva 
first name:
Larisa

location/conference:
SPPJT13

PRESENTATIONlink:
http://www.dfgspp1324.de/nuhagtools/event_NEW/dateien/SPPJT13/talks/Yaroslavtseva_JT13.pdf 
abstract:
We consider the problem of approximating the expectation
Ef(X(1)) of a function f of the solution X of a ddimensional system of stochastic differential equations (SDE) at time point 1. We present
a deterministic algorithm, which is based on a quadrature rule obtained by iteratively applying a
discretized WagnerPlaten step together with strategies to reduce the diameter and the size of the
support of a discrete measure. For Lipschitz continuous integrands f and smooth enough coefficients
of the SDE this algorithm almost achieves an error of order 1/d in terms of its computational cost.
We further present lower bounds for the error of arbitrary deterministic algorithms in worst case
settings with respect to classes of SDEs and classes of integrands defined in terms of smoothness
constraints. In particular, it turns out that our algorithm is almost asymptotically optimal.
This is joint work with Thomas MuellerGronbach (Passau) and Klaus Ritter (Kaiserslautern). 