Stochastic averaging problems with Gaussian forcing have been the subject of numerous studies, but far less attention has been paid to problems with infinite-variance stochastic forcing, such as an α-stable noise process. It has been shown that simple linear systems driven by correlated additive and multiplicative (CAM) Gaussian noise, which emerge in the context of reduced atmosphere and ocean dynamics, have infinite variance in certain parameter regimes. In this study, we consider the stochastic averaging of systems where a linear CAM noise process in the infinite variance parameter regime drives a comparatively slow process. We use (semi)-analytical approximations combined with numerical illustrations to compare the averaged process to one that is forced by a white α-stable process, demonstrating consistent properties in the case of large time-scale separation. We identify the conditions required for the fast linear CAM process to have such an influence in driving a slower process and then derive an (effectively) equivalent fast, infinite-variance process for which an existing stochastic averaging approximation is readily applied. The results are illustrated using numerical simulations of a set of example systems.
Skip Nav Destination
Article navigation
November 2017
Research Article|
November 09 2017
Reduced α-stable dynamics for multiple time scale systems forced with correlated additive and multiplicative Gaussian white noise
William F. Thompson;
William F. Thompson
a)
1
Department of Mathematics, University of British Columbia
, Vancouver, British Columbia V6T 1Z2, Canada
Search for other works by this author on:
Rachel A. Kuske;
Rachel A. Kuske
b)
2
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia
30332, USA
Search for other works by this author on:
Adam H. Monahan
Adam H. Monahan
c)
3
School of Earth and Ocean Science, University of Victoria
, Victoria, British Columbia V8W 3V6, Canada
Search for other works by this author on:
Chaos 27, 113105 (2017)
Article history
Received:
June 01 2017
Accepted:
October 06 2017
Citation
William F. Thompson, Rachel A. Kuske, Adam H. Monahan; Reduced α-stable dynamics for multiple time scale systems forced with correlated additive and multiplicative Gaussian white noise. Chaos 1 November 2017; 27 (11): 113105. https://doi.org/10.1063/1.4985675
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
Response to music on the nonlinear dynamics of human fetal heart rate fluctuations: A recurrence plot analysis
José Javier Reyes-Lagos, Hugo Mendieta-Zerón, et al.
Synchronization in spiking neural networks with short and long connections and time delays
Lionel Kusch, Martin Breyton, et al.
Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology
Eugene Tan, Shannon Algar, et al.
Related Content
Decoherence, Wave‐Function Collapses, Non‐Ordinary Statistical Mechanics and the Second Principle
AIP Conference Proceedings (November 2002)
Flexible two-point selection approach for characteristic function-based parameter estimation of stable laws
Chaos (July 2020)
Modeling climate change in Indonesia using VECM (vector error correction model)
AIP Conf. Proc. (February 2025)
On the compromise between noise reduction and speech/noise spatial information preservation in binaural speech enhancement
J. Acoust. Soc. Am. (May 2021)
On alpha stable distribution of wind driven water surface wave slope
Chaos (August 2008)