An H2-type error bound for balancing-related model order reduction of linear systems with Lévy noise

To solve a stochastic linear evolution equation numerically, finite dimensional approximations are commonly used. For a good approximation, one might end up with a sequence of ordinary stochastic linear differential equations of high order. To reduce the high dimension for practical computations, model order reduction is frequently used. Balanced truncation (BT) is a well-known technique from deterministic control theory and it was already extended for controlled linear systems with Lévy noise. Recently, a new ansatz was investigated which provides an alternative way to generalize BT for stochastic systems. There, the question of the existence of an H2-error bound was asked which we answer in this paper. We discuss how this bound can be computed practically and how to use it to find a suitable reduced order dimension.