Space-time transport schemes and homogenization. I. General theory of Markovian and non-Markovian processes

Motivated by the phenomenology of random particle motion in localized repulsive potentials or in periodic arrays of obstacles at low diusivities, the article introduces several classes of abstract transport schemes deriving from two basic prototypes, referred to as space-time and non-Markovian spin- driven diusion. The homogenization theory of these transport processes is developed and a closed-form expression for the eective velocity vector and the eective dispersion tensor obtained. Some applications are also presented.