Acceleration of test particles in one-dimensional random force fields

The aim of this research is to study acceleration of test particles in random space-time dependent force fields, by using or generalizing some tools developed in particular for the study of stochastic differential equations with time-dependent random parameters. Preliminary results given here are: a generalization of the Markov property to space-time, connected with a condition of non-repeated interaction, two-valued fields having this property allowing exact application of the widely used Bourret (or first order smoothing) approximation; the energy spectrum at exit of a bounded slab containing a space-dependent random field, the transmission coefficient of the slab and the mean energy gain of transmitted particles.