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Space-Time Correlations, within the Context of Stochastic Evolution

Costanza EF and Costanza G*

An extension of previous results is obtained concerning the evolution equations that satisfy not only the dynamical variables but the space-time correlations which constitute a hierarchy of differential equations. The stochastic evolution equations are Non-Markovian, and the corresponding Markovian evolution equations are obtained as a particular case when the evolution depends on the nearest previous time step. A relatively simple illustrative example is given allowing to obtain some previous results as limiting cases.