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Itô versus Stratonovich white-noise limits for systems with inertia and colored multiplicative noise

Kupferman, R. and Pavliotis, G. A. and Stuart, A. M. (2004) Itô versus Stratonovich white-noise limits for systems with inertia and colored multiplicative noise. Physical Review E, 70 (3). Art. No. 036120. ISSN 1539-3755. doi:10.1103/PhysRevE.70.036120. https://resolver.caltech.edu/CaltechAUTHORS:20170612-132002885

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Abstract

We consider the dynamics of systems in the presence of inertia and colored multiplicative noise. We study the limit where the particle relaxation time and the correlation time of the noise both tend to zero. We show that the limiting equation for the particle position depends on the magnitude of the particle relaxation time relative to the noise correlation time. In particular, the limiting equation should be interpreted either in the Itô or Stratonovich sense, with a crossover occurring when the two fast-time scales are of comparable magnitude. At the crossover the limiting stochastic differential equation is neither of Itô nor of Stratonovich type. This means that, after adiabatic elimination, the governing equations have different drift fields, leading to different physical behavior depending on the relative magnitude of the two fast-time scales. Our findings are supported by numerical simulations.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevE.70.036120DOIArticle
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.70.036120PublisherArticle
Additional Information:© 2004 American Physical Society. Received 28 October 2003; published 29 September 2004. The authors are grateful to D. Cai and J.C. Mattingly for useful suggestions. They are also grateful to J.M. Sancho for useful suggestions and for providing them with Refs. [3,11] and to P.R. Kramer for a very careful reading of an earlier version of this paper. G.A.P. and A.M.S. are grateful to EPSRC for financial support. R.K. was supported in part by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities and in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the U.S. Department of Energy under Contract DE-AC03-76-SF00098.
Funders:
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Israel Science FoundationUNSPECIFIED
Department of Energy (DOE)DE-AC03-76-SF00098
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ60
Issue or Number:3
Classification Code:PACS number(s): 02.50.Fz, 05.10.Gg, 05.40.Jc
DOI:10.1103/PhysRevE.70.036120
Record Number:CaltechAUTHORS:20170612-132002885
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170612-132002885
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78112
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 Jun 2017 20:51
Last Modified:15 Nov 2021 17:36

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