论文信息 - APPROXIMATION AND MODEL ORDER REDUCTION FOR SECOND ORDER SYSTEMS WITH LEVY-NOISE

APPROXIMATION AND MODEL ORDER REDUCTION FOR SECOND ORDER SYSTEMS WITH LEVY-NOISE

We consider a controlled second order stochastic partial differential equation (SPDE) with Levy noise. To solve this system numerically, we apply a Galerkin scheme leading to a sequence of ordinary SDEs of large order. To reduce the high dimension we use balanced truncation.

Peter Benner | Martin Redmann | P. Benner | Martin Redmann

[1] P. Kloeden,et al. The Numerical Approximation of Stochastic Partial Differential Equations , 2009 .

[2] Athanasios C. Antoulas,et al. Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.

[3] T. Damm. Rational Matrix Equations in Stochastic Control , 2004 .

[4] R. Curtain. STABILITY OF STOCHASTIC PARTIAL-DIFFERENTIAL EQUATION , 1981 .

[5] Jerzy Zabczyk,et al. Stochastic Partial Differential Equations with Lévy Noise: An Evolution Equation Approach , 2007 .

[6] A. J. Pritchard,et al. Stability and Stabilizability of Infinite-Dimensional Systems , 1981 .

[7] Peter Benner,et al. Model reduction for stochastic systems , 2015 .

[8] P. Kloeden,et al. Time-discretised Galerkin approximations of parabolic stochastic PDE's , 1996, Bulletin of the Australian Mathematical Society.

[9] E. Hausenblas. Approximation for Semilinear Stochastic Evolution Equations , 2003 .

[10] Peter Benner,et al. Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems , 2011, SIAM J. Control. Optim..

[11] B. Moore. Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .