Strong Convergence in the Stochastic Averaging Principle.

• Author(s) / Creator(s)

  • Heunis, A. J.
  • Kouritzin, Michael

• 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

• Subjects / Keywords

  • Mathematics
  • Stochastic averaging principle
  • Applied mathematics

• Type of Item

  Article (Published)

• DOI

  https://doi.org/10.7939/R3QR4NR63

• License

  © 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.