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Aquino T, Aubeneau A, McGrath G, et al. Noise-Driven Return Statistics: Scaling and Truncation in Stochastic Storage Processes. Sci Rep. 2017;7(1):302doi: 10.1038/s41598-017-00451-x.
Aquino, T., Aubeneau, A., McGrath, G., Bolster, D., & Rao, S. (2017). Noise-Driven Return Statistics: Scaling and Truncation in Stochastic Storage Processes. Scientific reports, 7(1), 302. https://doi.org/10.1038/s41598-017-00451-x
Aquino, Tomás, et al. "Noise-Driven Return Statistics: Scaling and Truncation in Stochastic Storage Processes." Scientific reports vol. 7,1 (2017): 302. doi: https://doi.org/10.1038/s41598-017-00451-x
Aquino T, Aubeneau A, McGrath G, Bolster D, Rao S. Noise-Driven Return Statistics: Scaling and Truncation in Stochastic Storage Processes. Sci Rep. 2017 Mar 22;7(1):302. doi: 10.1038/s41598-017-00451-x. PMID: 28331189; PMCID: PMC5428502.
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Sci Rep. 2017 Mar 22;7(1):302. doi: 10.1038/s41598-017-00451-x.

Noise-Driven Return Statistics: Scaling and Truncation in Stochastic Storage Processes.

Scientific reports

Tomás Aquino, Antoine Aubeneau, Gavan McGrath, Diogo Bolster, Suresh Rao

Affiliations

  1. Department of Civil & Environmental Engineering and Earth Sciences, University of Notre Dame, 46556, Indiana, USA. [email protected].
  2. Lyles School of Civil Engineering, Purdue University, 47907, Indiana, USA.
  3. Ishka Solutions, Western Australia, Australia.
  4. Department of Civil & Environmental Engineering and Earth Sciences, University of Notre Dame, 46556, Indiana, USA.

PMID: 28331189 PMCID: PMC5428502 DOI: 10.1038/s41598-017-00451-x

Abstract

In countless systems, subjected to variable forcing, a key question arises: how much time will a state variable spend away from a given threshold? When forcing is treated as a stochastic process, this can be addressed with first return time distributions. While many studies suggest exponential, double exponential or power laws as empirical forms, we contend that truncated power laws are natural candidates. To this end, we consider a minimal stochastic mass balance model and identify a parsimonious mechanism for the emergence of truncated power law return times. We derive boundary-independent scaling and truncation properties, which are consistent with numerical simulations, and discuss the implications and applicability of our findings.

References

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