  Generalized Langevin equations (GLE) with multiplicative white Poisson noise
pose the usual prescription dilemma leading to different evolution equations
(master equations) for the probability distribution. Contrary to the case of
multiplicative gaussian white noise, the Stratonovich prescription does not
correspond to the well known mid-point (or any other intermediate)
prescription. By introducing an inertial term in the GLE we show that the Ito
and Stratonovich prescriptions naturally arise depending on two time scales,
the one induced by the inertial term and the other determined by the jump
event. We also show that when the multiplicative noise is linear in the random
variable one prescription can be made equivalent to the other by a suitable
transformation in the jump probability distribution. We apply these results to
a recently proposed stochastic model describing the dynamics of primary soil
salinization, in which the salt mass balance within the soil root zone requires
the analysis of different prescriptions arising from the resulting stochastic
differential equation forced by multiplicative white Poisson noise whose
features are tailored to the characters of the daily precipitation. A method is
finally suggested to infer the most appropriate prescription from the data.
