Abstract
Continuum partial differential equations are obtained from a set of discrete stochastic evolution equations of both non-Markovian and Markovian processes and applied to the diffusion on a cubic lattice within the context of the lattice gas model. A procedure allowing to construct one-dimensional lattices that are topologically equivalent to a cubic three-dimensional lattice is described in detail using a successive “unfolding” process. This example shows some new features that possess the procedure and extensions are also suggested in order to provide some another uses of the present approach.
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