Display options
Cite
Sire C. Crossing intervals of non-Markovian Gaussian processes. Phys Rev E Stat Nonlin Soft Matter Phys. 2008;78(1):011121doi: 10.1103/PhysRevE.78.011121.
Sire, C. (2008). Crossing intervals of non-Markovian Gaussian processes. Physical review. E, Statistical, nonlinear, and soft matter physics, 78(1), 011121. https://doi.org/10.1103/PhysRevE.78.011121
Sire, Clément. "Crossing intervals of non-Markovian Gaussian processes." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 78,1 (2008): 011121. doi: https://doi.org/10.1103/PhysRevE.78.011121
Sire C. Crossing intervals of non-Markovian Gaussian processes. Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jul;78(1):011121. doi: 10.1103/PhysRevE.78.011121. Epub 2008 Jul 23. PMID: 18763933.
Copy Download .nbib Format: NLM
Share it on

Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jul;78(1):011121. doi: 10.1103/PhysRevE.78.011121. Epub 2008 Jul 23.

Crossing intervals of non-Markovian Gaussian processes.

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

Clément Sire

Affiliations

  1. Laboratoire de Physique Théorique--IRSAMC, CNRS, Université Paul Sabatier, 31062 Toulouse, France. [email protected]

PMID: 18763933 DOI: 10.1103/PhysRevE.78.011121

Abstract

We review the properties of time intervals between the crossings at a level M of a smooth stationary Gaussian temporal signal. The distribution of these intervals and the persistence are derived within the independent interval approximation (IIA). These results grant access to the distribution of extrema of a general Gaussian process. Exact results are obtained for the persistence exponents and the crossing interval distributions, in the limit of large |M|. In addition, the small-time behavior of the interval distributions and the persistence is calculated analytically, for any M. The IIA is found to reproduce most of these exact results, and its accuracy is also illustrated by extensive numerical simulations applied to non-Markovian Gaussian processes appearing in various physical contexts.

Publication Types