Effect of different jump distributions on the dynamics of jump processes

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Abstract

The paper investigates stochastic processes forced by independent and identically distributed jumps occurring according to a Poisson process. The impact of different distributions of the jump amplitudes are analyzed for processes with linear drift. Exact expressions of the probability density functions are derived when jump amplitudes are distributed as exponential, gamma, and mixture of exponential distributions for both natural and reflecting boundary conditions. The mean level-crossing properties are studied in relation to the different jump amplitudes. As an example of application of the previous theoretical derivations, the role of different rainfall-depth distributions on an existing stochastic soil water balance model is analyzed. It is shown how the shape of distribution of daily rainfall depths plays a more relevant role on the soil moisture probability distribution as the rainfall frequency decreases, as predicted by future climatic scenarios.

Original languageEnglish (US)
Article number061133
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume81
Issue number6
DOIs
StatePublished - Jun 28 2010

All Science Journal Classification (ASJC) codes

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

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