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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the tangent flow of a stochastic differential equation with fast drift


Author: Richard B. Sowers
Journal: Trans. Amer. Math. Soc. 353 (2001), 1321-1334
MSC (1991): Primary 60H10
Published electronically: December 18, 2000
MathSciNet review: 1806739
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Abstract:

We investigate the behavior of the tangent flow of a stochastic differential equation with a fast drift. The state space of the stochastic differential equation is the two-dimensional cylinder. The fast drift has closed orbits, and we assume that the orbit times vary nontrivially with the axial coordinate. Under a nondegeneracy assumption, we find the rate of growth of the tangent flow. The calculations involve a transformation introduced by Pinsky and Wihstutz.


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Additional Information

Richard B. Sowers
Affiliation: Department of Mathematics, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801
Email: r-sowers@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02773-2
PII: S 0002-9947(00)02773-2
Keywords: Floquet, Lyapunov exponent, Pinsky-Wihstutz, stochastic averaging
Received by editor(s): September 21, 1999
Received by editor(s) in revised form: July 20, 2000
Published electronically: December 18, 2000
Additional Notes: This work was supported by NSF DMS 9615877. The author would like to thank Professor Sri Namachchivaya of the Department of Aeronautical and Astronautical Engineering at the University of Illinois at Urbana-Champaign for pointing out the paper by Pinsky and Wihstutz. The author would also like to thank the anonymous referee who insisted upon notational clarity.
Article copyright: © Copyright 2000 American Mathematical Society