  The noisy dynamics of chemical systems is commonly studied using either the
chemical master equation (CME) or the chemical Fokker-Planck equation (CFPE).
The latter is a continuum approximation of the discrete CME approach. We here
show that the CFPE may fail to capture the CME's prediction of noise-induced
multistability. In particular we find a simple chemical system for which the
CME's marginal probability distribution changes from unimodal to multimodal as
the system-size decreases below a critical value, while the CFPE's marginal
probability distribution is unimodal for all physically meaningful system
sizes.
