# Preprint No. MPIMD/14-03

#### Author(s): Martin Redmann, Peter Benner

#### Email: redmann@mpi-magdeburg.mpg.de

#### Date: 2014-02-13

#### Abstract:

To solve a stochastic linear evolution equation numerically, finite dimensional approximations are commonly used. If one uses the well known Galerkin scheme one can end up with a sequence of ordinary stochastic linear equations of high order. To reduce the high dimension for practical computations we consider balanced truncation being a model order reduction technique known from deterministic control theory. So, we generalize balanced truncation for controlled linear systems with Levy noise, discuss properties of the reduced order model, provide an error bound and give some examples.

#### BibTeX:

@TECHREPORT{MPIMD14-03,

author = {Martin Redmann and Peter Benner},

title = {Model Reduction for Stochastic Systems},

number = {MPIMD/14-03},

month = feb,

year = 2014,

institution = {Max Planck Institute Magdeburg},

type = {Preprint},

note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},

}