On the tangent flow of a stochastic differential equation with fast drift
Author:
Richard B. Sowers
Journal:
Trans. Amer. Math. Soc. 353 (2001), 13211334
MSC (1991):
Primary 60H10
Published electronically:
December 18, 2000
MathSciNet review:
1806739
Fulltext PDF Free Access
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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 twodimensional 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:
rsowers@math.uiuc.edu
DOI:
http://dx.doi.org/10.1090/S0002994700027732
PII:
S 00029947(00)027732
Keywords:
Floquet,
Lyapunov exponent,
PinskyWihstutz,
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 UrbanaChampaign 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
