  Along the ideas of Curtain and Glover, we extend the balanced truncation
method for infinite-dimensional linear systems to bilinear and stochastic
systems. Specifically , we apply Hilbert space techniques used in many-body
quantum mechanics to establish error bounds for the truncated system and prove
convergence results. The functional analytic setting allows us to obtain mixed
Hardy space error bounds for both finite-and infinite-dimensional systems, and
it is then applied to the model reduction of stochastic evolution equations
driven by Wiener noise.
