Probabilistic dynamics of some jump-diffusion systems.


Journal Article

Some exact solutions to the forward Chapman-Kolmogorov equation are derived for processes driven by both Gaussian and compound Poisson (shot) noise. The combined action of these two forms of white noise is analyzed in transient and equilibrium conditions for different jump distributions and additive Gaussian noise. Steady-state distributions with power-law tails are obtained for exponentially distributed jumps and multiplicative linear Gaussian noise. Two applications are discussed: namely, the virtual waiting-time or Takàcs process including Gaussian oscillations and a simplified model of soil moisture dynamics, in which rainfall is modeled as a compound Poisson process and fluctuations in potential evapotranspiration are Gaussian.

Full Text

Duke Authors

Cited Authors

  • Daly, E; Porporato, A

Published Date

  • February 7, 2006

Published In

Volume / Issue

  • 73 / 2 Pt 2

Start / End Page

  • 026108 -

PubMed ID

  • 16605399

Pubmed Central ID

  • 16605399

Electronic International Standard Serial Number (EISSN)

  • 1550-2376

International Standard Serial Number (ISSN)

  • 1539-3755

Digital Object Identifier (DOI)

  • 10.1103/physreve.73.026108


  • eng