Singular perturbation approximation for linear systems with Lévy noise

DOI10.1142/S0219493718500338zbMath1394.60047OpenAlexW2743905828MaRDI QIDQ4584284

Martin Redmann, Peter Benner

Publication date: 29 August 2018

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219493718500338

zbMATH Keywords

Lévy processessingular perturbation approximationbalancing related model order reductionlinear controlled stochastic systems

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic systems in control theory (general) (93E03) Model reduction in optics and electromagnetic theory (78M34)

Related Items (7)

Model reduction of controlled Fokker-Planck and Liouville-von Neumann equations ⋮ Model order reduction for bilinear systems with non-zero initial states – different approaches with error bounds ⋮ Energy estimates and model order reduction for stochastic bilinear systems ⋮ Balanced model order reduction for linear random dynamical systems driven by Lévy noise ⋮ Optimization based model order reduction for stochastic systems ⋮ Bilinear Systems---A New Link to $\mathcal H_2$-norms, Relations to Stochastic Systems, and Further Properties ⋮ A new type of singular perturbation approximation for stochastic bilinear systems

Cites Work

• Approximation and model order reduction for second order systems with Levy-noise
• Positive operators and stable truncation
• An averaging principle for stochastic dynamical systems with Lévy noise
• Model reduction for stochastic systems
• Rational matrix equations in stochastic control.
• Model reduction for control system design
• Approximation for semilinear stochastic evolution equations
• A concise course on stochastic partial differential equations
• Balanced Averaging of Bilinear Systems with Applications to Stochastic Control
• Dual Pairs of Generalized Lyapunov Inequalities and Balanced Truncation of Stochastic Linear Systems
• Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems
• Stochastic Averaging of Dynamical Systems with Multiple Time Scales Forced with $\alpha$-Stable Noise
• Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space–time noise
• Principal component analysis in linear systems: Controllability, observability, and model reduction
• Singular perturbational model reduction of balanced systems
• Singular perturbation approximation of balanced systems
• Time-discretised Galerkin approximations of parabolic stochastic PDE's
• Noise-Induced Phenomena in Slow-Fast Dynamical Systems
• Stochastic Partial Differential Equations with Levy Noise
• Approximation of Large-Scale Dynamical Systems
• Stochastic Equations in Infinite Dimensions

This page was built for publication: Singular perturbation approximation for linear systems with Lévy noise