Relative-error bound for discrete balanced stochastic truncation

Abstract

Fundamental differences between discrete-time balanced stochastic truncation (BST) and its continuous-time counterpart are shown to preclude a straightforward application of bilinear mappings for directly generalizing existing continuous-time error bounds. Nevertheless, discrete-time BST is shown to satisfy precisely the same L_k error bound as continuous-time BST, although the discrete-time derivations are somewhat more complex.