Extension of the JIMWLK equation in the low gluon density region

Abstract It has recently been realized that the Balitsky-JIMWLK equations have serious shortcomings as equations to be used in small- x evolution near the unitarity limit. A recent generalization of the Balitsky equations has been given which corrects these shortcomings. In this paper we present an equivalent discussion, but in terms of the JIMWLK equation where we show that a new (fourth order functional derivative) term should be included. We also present a stochastic version of the new equation which, however, has some unusual mathematical aspects which are not as yet well understood.