  Resummations of soft gluon emissions play an important role in many
applications of QCD, among them jet observables and small x saturation effects.
Banfi, Marchesini, and Smye have derived an evolution equation for non-global
jet observables that exhibits a remarkable analogy with the BK equation used in
the small x context. Here, this analogy is used to generalize the former beyond
the leading N_c approximation. The result shows striking analogy with the
JIMWLK equation describing the small x evolution of the color glass condensate.
A Langevin description allows numerical implementation and provides clues for
the formulation of closed forms for amplitudes at finite N_c. The proof of the
new equation is based on these amplitudes with ordered soft emission. It is
fully independent of the derivation of the JIMWLK equation and thus sheds new
light also on this topic.
