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is. A formidable task is also to characterize the relation between the outcome of
micro-simulations and the results of the stochastic analysis.
We have also presented an approximation using bi-variate distributions for
2-D automata with von Neumann neighborhood. Our approximation consists of
difference equations. These equations can easily be generated on a com-
puter and iteratively solved. Thus our mesoscopic analysis will mainly be based
on numerical computations. Analytical expressions can be obtained for homo-
geneous distributions only, i.e distributions which do not depend on the position
of individual cells.
The method we have used for the approximations is now improved in scien-
tific disciplines as different as approximate reasoning, probabilistic logic, graph-
ical models in statistics, and optimization by search distributions [13]. We are
confident that by using new results we will derive a practical method for the
stochastic analysis of cellular automata and stochastic cellular automata.
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