Prescription-induced jump distributions in multiplicative Poisson processes

Samir Suweis, Amilcare Michele M. Porporato, Andrea Rinaldo, Amos Maritan

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


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 midpoint (or any other intermediate) prescription. By introducing an inertial term in the GLE, we show that the Itô and Stratonovich prescriptions naturally arise depending on two time scales, 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, the features of which are tailored to the characters of the daily precipitation. A method is finally suggested to infer the most appropriate prescription from the data.

Original languageEnglish (US)
Article number061119
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number6
StatePublished - Jun 15 2011

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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