Preprint No. MPIMD/15-20

Title: An ℋ₂-Type Error Bound for Balancing-Related Model Order Reduction of Linear Systems with L\'evy Noise

Author(s): Martin Redmann, Peter Benner

Email: redmann@mpi-magdeburg.mpg.de

Date: 2015-12-17

Abstract:

To solve a stochastic linear evolution equation numerically, finite dimensional approximations are commonly used. For a good approximation, one might end up with a sequence of ordinary stochastic linear equations of high order. To reduce the high dimension for practical computations, model order reduction is frequently used. Balanced truncation (BT) is a well-known technique from deterministic control theory and it was already extended for controlled linear systems with Levy noise. Recently, a new ansatz was investigated which provides an alternative way to generalize BT for stochastic systems. There, the question of the existence of an ℋ₂-error bound was asked which we answer in this paper.

BibTeX:

@TECHREPORT{MPIMD15-20,
author = {Martin Redmann and Peter Benner},
title = {An ℋ₂-Type Error Bound for Balancing-Related Model Order Reduction of Linear Systems with L\'evy Noise},
number = {MPIMD/15-20},
month = dec,
year = 2015,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}


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