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Balanced model order reduction for linear systems driven by Lévy noise

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UNQ - Uncertainty quantification for complex systems: theory and methodologies

When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used. Balanced truncation (BT) is a well-known projection technique in the deterministic framework which reduces the order of a control system and hence reduces computational complexity. We give an introduction to model order reduction (MOR) by BT and then consider a differential equation where 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 MOR of linear stochastic differential equations with additive L'evy noise. Moreover, we derive error bounds for BT and provide numerical results for a specific example which support the theory. This is joint work with Martin Redmann (WIAS Berlin).

This talk is part of the Isaac Newton Institute Seminar Series series.

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