A topological theorem and correlations, within the context of stochastic evolution

A topological theorem, that proves that any d-dimensional lattice is equivalent to a one-dimensional one, allows to write the evolution equations as a function of only one spatial coordinate. Stochastic and continuum deterministic evolution equations, are derived from a set of discrete stochastic evolution equations. The evolution equations of the dynamical variables and correlations are obtained for processes that evolve non-Markovianly. Some relatively simple examples are given in order to illustrate the procedures.