eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-04-19
1
37
10.4230/DagSemProc.04401.6
article
Lower Bounds and Non-Uniform Time Discretization for Approximation of Stochastic Heat Equations
Ritter, Klaus
Müller-Gronbach, Thomas
We study algorithms for approximation of the mild solution
of stochastic heat equations on the spatial domain ]0,1[^d.
The error of an algorithm is defined in L_2-sense.
We derive lower bounds for the error of every algorithm
that uses a total of N evaluations of one-dimensional components
of the driving Wiener process W. For equations with additive
noise we derive matching upper bounds and we construct
asymptotically optimal algorithms. The error bounds depend on
N and d, and on the decay of eigenvalues of the covariance of W
in the case of nuclear noise. In the latter case the use of
non-uniform time discretizations is crucial.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol04401/DagSemProc.04401.6/DagSemProc.04401.6.pdf
Stochastic heat equation
Non-uniform time discretization
minimal errors
upper and lower bounds