  When solving linear stochastic differential equations numerically, usually a
high order spatial discretisation is used. Balanced truncation (BT) and
singular perturbation approximation (SPA) are well-known projection techniques
in the deterministic framework which reduce the order of a control system and
hence reduce computational complexity. This work considers both methods when
the control is replaced by a noise term. We provide theoretical tools such as
stochastic concepts for reachability and observability, which are necessary for
balancing related model order reduction of linear stochastic differential
equations with additive L\'evy noise. Moreover, we derive error bounds for both
BT and SPA and provide numerical results for a specific example which support
the theory.
