  A stochastic algorithm for simulation of fluctuation-induced kinetics of
H$_2$ formation on grain surfaces is suggested as a generalization of the
technique developed in our recent studies where this method was developed to
describe the annihilation of spatially separate electrons and holes in a
disordered semiconductor. The stochastic model is based on the spatially
inhomogeneous, nonlinear integro-differential Smoluchowski equations with
random source term. In this paper we derive the general system of Smoluchowski
type equations for the formation of H$_2$ from two hydrogen atoms on the
surface of interstellar dust grains with physisorption and chemisorption sites.
We focus in this study on the spatial distribution, and numerically investigate
the segregation in the case of a source with a continuous generation in time
and randomly distributed in space. The stochastic particle method presented is
based on a probabilistic interpretation of the underlying process as a
stochastic Markov process of interacting particle system in discrete but
randomly progressed time instances. The segregation is analyzed through the
correlation analysis of the vector random field of concentrations which appears
to be isotropic in space and stationary in time.
