Continuous upscaling and averaging

The procedure of upscaling/averaging the values and equations continuum mechanics appears in many scientific areas. Traditionally, upscaling is carried out by a “jump” between two distant scales. We suggest an alternative for gradual upscaling, with continuous transition from finer to coarser scale along axis, averaging on way. It shown, natural assumptions, that this similar Markov process described Ornstein-Uhlenbeck equation. This only option, unlike traditional weight averaging, where multiple functions are possible. An interpretation provided, solution equation obtained. demonstrate also that, under conservation laws flow expressed divergent form, fluxes upscaled same rules as densities. As example, diffusion coefficient derived.