  Spatially-distributed, nonequilibrium chemical systems described by a Markov
chain model are considered. The evolution of such systems arises from a
combination of local birth-death reactive events and random walks executed by
the particles on a lattice. The parameter \gamma, the ratio of characteristic
time scales of reaction and diffusion, is used to gauge the relative
contributions of these two processes to the overall dynamics. For the case of
relatively fast diffusion, i.e. \gamma << 1, an approximate solution to the
Markov chain in the form of a perturbation expansion in powers of \gamma is
derived. Kinetic equations for the average concentrations differ from the
mass-action law and contain memory terms. For a reaction- diffusion system with
Willamowski-Rossler reaction mechanism, we further derive the following two
results: a) in the limit of \gamma --> 0 these memory terms vanish and the
mass-action law is recovered; b) the memory kernel is found to assume a simple
exponential form. A comparison with numerical results from lattice gas
automaton simulations is also carried out.
