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Strong Convergence in the Stochastic Averaging Principle. Open Access

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Author or creator
Heunis, A. J.
Kouritzin, Michael
Additional contributors
Subject/Keyword
mathematics
stochastic averaging principle
applied mathematics
Type of item
Journal Article (Published)
Language
English
Place
Time
Description
In this note we consider the almost sure convergence (as ϵ→0) of solution Xϵ(·), defined over the interval 0 ≤ τ ≤ 1, of the random ordinary differential equation View the MathML source Here {F(x, t, ω), t ≥ 0} is a strong mixing process for each x and (x, t) → F(x, t, ω) is subject to regularity conditions which ensure the existence of a unique solution over 0 ≤ τ ≤ 1 for all ϵ > 0. Under rather weak conditions it is shown that the function Xϵ(·, ω) converges a.s. to the solution x0(·) of a non-random averaged differential equation View the MathML source the convergence being uniform over 0 ≤ τ ≤ 1.
Date created
1994
DOI
doi:10.7939/R3QR4NR63
License information
Rights
© 1994 Journal of Mathematical Analysis and Applications. This version of this article is open access and can be downloaded and shared. The original author(s) and source must be cited. Non-commercial use only.
Citation for previous publication
A.J. Heunis, M.A. Kouritzin, Strong Convergence in the Stochastic Averaging Principle, Journal of Mathematical Analysis and Applications, Volume 187, Issue 1, 1 October 1994, Pages 134-155, ISSN 0022-247X,  http://dx.doi.org/10.1006/jmaa.1994.1349
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