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T. Sickenberger, E. Weinmüller, R. Winkler:
"Local error estimates for moderately smooth problems: Part II - SDEs and SDAEs with small noise";
in: "ASC Report 17/2007", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2007, ISBN: 978-3-902627-00-1.

The paper consists of two parts. In the first part of the paper, we proposed a
procedure to estimate local errors of low order methods applied to solve initial value
problems in ordinary differential equations (ODEs) and index-1 differential-algebraic
equations (DAEs). Based on the idea of Defect Correction we developed local error
estimates for the case when the problem data is only moderately smooth, which is
typically the case in stochastic differential equations. In this second part, we will
consider the estimation of local errors in context of mean-square convergent methods
for stochastic differential equations (SDEs) with small noise and index-1 stochastic
differential-algebraic equations (SDAEs). Numerical experiments illustrate the performance
of the mesh adaptation based on the local error estimation developed in this
paper.

local error estimation · step-size control · adaptive methods · stochastic

http://www.asc.tuwien.ac.at/preprint/2007/asc17x2007.pdf