Balanced model order reduction for linear random dynamical systems driven by Lévy noise

Martin Redmann, Melina A. Freitag

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used. Balanced truncation (BT) and singular perturbation approximation (SPA) are well-known projection techniques in the deterministic framework which reduce the order of a control system and hence reduce computational complexity. This work considers both methods when the control is replaced by a noise term. We provide theoretical tools such as stochastic concepts for reachability and observability, which are necessary for balancing related model order reduction of linear stochastic differential equations with additive Lévy noise. Moreover, we derive error bounds for both BT and SPA and provide numerical results for a specific example which support the theory.

Original languageEnglish
Pages (from-to)33-59
Number of pages27
JournalJournal of Computational Dynamics
Volume5
Issue number1 & 2
DOIs
Publication statusPublished - 1 Dec 2018

Keywords

  • Balanced truncation
  • Gramians
  • Lyapunov equations
  • Lévy processes
  • Model order reduction
  • Singular perturbation approximation
  • Stochastic systems

ASJC Scopus subject areas

  • Computational Mechanics
  • Computational Mathematics

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