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Phys. Rev. E 63, 036105 (2001) [8 pages]

Mean first passage times of processes driven by white shot noise

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F. Laio1,2, A. Porporato1,2, L. Ridolfi1, and I. Rodriguez-Iturbe2
1Dipartimento di Idraulica Trasporti e Infrastrutture Civili, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
2Department of Civil and Environmental Engineering and Center for Energy and Environmental Studies, Princeton University, Princeton, New Jersey 08544

Received 25 October 2000; published 20 February 2001

We consider mean first passage times in systems driven by white shot noise with exponentially distributed jump heights. Simple interpretable results are obtained and the linkage between those results and the steady-state probability density function of the process is presented. The virtual waiting-time or Takács process (constant losses) and the shot noise process with linear losses are analyzed in depth, along with a more complex process with useful implications for the modeling of the soil moisture dynamics in hydrology.


©2001 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevE.63.036105
DOI: 10.1103/PhysRevE.63.036105
PACS: 02.50.-r, 05.40.-a, 89.60.-k

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