Balanced model reduction of partially-observed Langevin processes: an averaging principle

Abstract

We study balanced model reduction of partially-observed linear stochastic dierential equations of Langevin type. Balancing the equations of motion gives rise to a singularly perturbed system of equations with slow and fast degrees of freedom, and we prove that in the limit of the fast variables becoming innitely fast, the solutions converge to the solution of a reduced-order Langevin equation. We illustrate the method with several numerical examples and discuss the relation to model reduction of deterministic control systems that have an underlying Hamiltonian structure.