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Effect of different jump distributions on the dynamics of jump processes.

Publication ,  Journal Article
Daly, E; Porporato, A
Published in: Physical review. E, Statistical, nonlinear, and soft matter physics
June 2010

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.

Duke Scholars

Published In

Physical review. E, Statistical, nonlinear, and soft matter physics

DOI

EISSN

1550-2376

ISSN

1539-3755

Publication Date

June 2010

Volume

81

Issue

6 Pt 1

Start / End Page

061133

Related Subject Headings

  • Fluids & Plasmas
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Daly, E., & Porporato, A. (2010). Effect of different jump distributions on the dynamics of jump processes. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 81(6 Pt 1), 061133. https://doi.org/10.1103/physreve.81.061133
Daly, Edoardo, and Amilcare Porporato. “Effect of different jump distributions on the dynamics of jump processes.Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 81, no. 6 Pt 1 (June 2010): 061133. https://doi.org/10.1103/physreve.81.061133.
Daly E, Porporato A. Effect of different jump distributions on the dynamics of jump processes. Physical review E, Statistical, nonlinear, and soft matter physics. 2010 Jun;81(6 Pt 1):061133.
Daly, Edoardo, and Amilcare Porporato. “Effect of different jump distributions on the dynamics of jump processes.Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol. 81, no. 6 Pt 1, June 2010, p. 061133. Epmc, doi:10.1103/physreve.81.061133.
Daly E, Porporato A. Effect of different jump distributions on the dynamics of jump processes. Physical review E, Statistical, nonlinear, and soft matter physics. 2010 Jun;81(6 Pt 1):061133.

Published In

Physical review. E, Statistical, nonlinear, and soft matter physics

DOI

EISSN

1550-2376

ISSN

1539-3755

Publication Date

June 2010

Volume

81

Issue

6 Pt 1

Start / End Page

061133

Related Subject Headings

  • Fluids & Plasmas
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences