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Reply to "comment on 'Monte Carlo simulations for a Lotka-type model with reactant surface diffusion and interactions' ".

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As is well known, a wide class of physical problems, including the kinetics of heterogeneous catalytic reactions, is traditionally described in terms of the master equations ~ME!. The definition of ME allows us not only to perform Monte Carlo ~MC! simulations, but also to develop at the same time appropriate analytical methods @mean field~MF!, cluster approximations, etc. #@ 1#. ME is formally defined when all possible states of a system and the transition rates between these states are specified. This is enough to define only the transition rates K(i! j ) for such elementary processes as particle adsorption, desorption, diffusion, reaction, etc., from the initial state i to the final state j. ME is a purely axiomatic theory, e.g., the actual form of the transition rates K(i! j ) is completely arbitrary. When neglecting adsorbateadsorbate lateral interaction ~AALI!, various MC methods have to give ~and indeed they give! essentially the same reaction kinetics ~if we neglect unavoidable fluctuation effects!. For illustration, the MC methods used in Refs. @2,3# differ from one another as considerably as standard random walks differ from continuous-time random walks @4#. However, both methods give the equivalent kinetics @5# when