On the stochastic parametrization of short-scale processes

Stochastic parametrization of short-scale processes is revisited in an idealized setting in which the short scales are manifested as small-amplitude deterministic forcings acting on the evolution laws of the resolved variables. Conditions under which the invariant probability density of the original deterministic system tends to that induced by the action of appropriately parametrized Gaussian white noise are identified. On the other hand, substantial differences are revealed between the deterministic description and its stochastic substitute when time-dependent properties are considered such as short-time behaviour of the variance, recurrence and first passage time statistics. Illustrations and explicit evaluations are provided on low-order model systems.SCOPUS: ar.jDecretOANoAutActif