@article{KuhlbrodtMonahan2003,
  author    = {Kuhlbrodt, Till and Monahan, A. H.},
  title     = {Stochastic stability of open-ocean deep convection},
  issn      = {0022-3670},
  year      = {2003},
  abstract  = {Open-ocean deep convection is a highly variable and strongly nonlinear process that plays an essential role in the global ocean circulation. A new view of its stability is presented here, in which variability, as parameterized by stochastic forcing, is central. The use of an idealized deep convection box model allows analytical solutions and straightforward conceptual understanding while retaining the main features of deep convection dynamics. In contrast to the generally abrupt stability changes in deterministic systems, measures of stochastic stability change smoothly in response to varying forcing parameters. These stochastic stability measures depend chiefly on the residence times of the system in different regions of phase space, which need not contain a stable steady state in the deterministic sense. Deep convection can occur frequently even for parameter ranges in which it is deterministically unstable; this effect is denoted wandering unimodality. The stochastic stability concepts are readily applied to other components of the climate system. The results highlight the need to take climate variability into account when analyzing the stability of a climate state},
  language  = {en}
}
@article{GairingHogeleKosenkovaetal.2017,
  author    = {Gairing, Jan M. and Hogele, Michael A. and Kosenkova, Tania and Monahan, Adam H.},
  title     = {How close are time series to power tail Levy diffusions?},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {27},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.4986496},
  pages     = {20},
  year      = {2017},
  abstract  = {This article presents a new and easily implementable method to quantify the so-called coupling distance between the law of a time series and the law of a differential equation driven by Markovian additive jump noise with heavy-tailed jumps, such as a-stable Levy flights. Coupling distances measure the proximity of the empirical law of the tails of the jump increments and a given power law distribution. In particular, they yield an upper bound for the distance of the respective laws on path space. We prove rates of convergence comparable to the rates of the central limit theorem which are confirmed by numerical simulations. Our method applied to a paleoclimate time series of glacial climate variability confirms its heavy tail behavior. In addition, this approach gives evidence for heavy tails in datasets of precipitable water vapor of the Western Tropical Pacific. Published by AIP Publishing.},
  language  = {en}
}