  Using Monte Carlo integration techniques, we investigate running coupling
effects compatible with the high energy bootstrap condition to all orders in
the strong coupling in evolution equations valid at small values of Bjorken x
in deep inelastic scattering. A model for the running of the coupling with
analytic behavior in the infrared region and compatible with power corrections
to jet observables is used. As a difference to the fixed coupling case, where
the momentum transfer acts as an effective strong cut-off of the diffusion to
infrared scales, in our running coupling study the dependence on the momentum
transfer is much milder.
