SPDEs with Levy noise can be used to model chemical, physical or biological
phenomena which contain uncertainties. In this talk, we consider
semi-discretised versions of these SPDEs which might be of large order. The
goal is to save computational time by replacing large scale systems by systems
of low order capturing the main information.

In particular, we investigate stochastic heat and damped wave equations which
we approximate by a Galerkin scheme. This leads to high dimensional ordinary
SDEs. We reduce this dimension by using balancing related model order
reduction (MOR) techniques which are well-known from the deterministic control
theory and can be extended to stochastic equations as well. The idea of
balancing a system is to create a system where the dominant reachable and
observable states are the same. Afterwards, the diffcult to observe and
diffcult to reach states are neglected to obtain a reduced order model.

In this talk, we discuss balanced truncation and the singular perturbation
approximation for stochastic equations with Levy noise which are balancing
related MOR techniques. We compare these methods, summarise already existing
results and discuss recent achievements.