Deterministic balancing and stochastic model reduction

A recent approach to the deterministic model reduction problem is based on the notion of balancing. However, the original development of deterministic balancing did not contain any statistical considerations with which to develop a stochastic model reduction algorithm. Nevertheless, it is shown in this note that there are two stochastic model reduction algorithms in the literature which result in a deterministically balanced model. Their equivalence with deterministic balancing provides a stochastic interpretation to the deterministic algorithm.