  We elucidate a new technique for estimating the production of multiple (at
least two) hard jets in Higgs production via gluon-gluon fusion. The approach
is based upon high energy factorisation, with the region of applicability
extended by constraints on the analytic behaviour of the scattering amplitudes
stemming from known all-order results. The method approximates both real and
virtual corrections, and allows for the resummation in an n-parton inclusive
event sample of the terms dominant in the high energy limit. The resulting
approximation is matched to the known tree level matrix elements for the
production of a Higgs boson in association with 2 and 3 jets, and implemented
in a Monte Carlo generator. Example results are presented and characteristic
radiation patterns discussed.
