Averaging principle and normal deviations for multi-scale stochastic hyperbolic-parabolic equations
Röckner M, Xie L, Yang L (2022)
Stochastics and Partial Differential Equations: Analysis and Computations .
Zeitschriftenaufsatz
| E-Veröff. vor dem Druck | Englisch
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Autor*in
Röckner, MichaelUniBi;
Xie, Longjie;
Yang, Li
Einrichtung
Abstract / Bemerkung
We study the asymptotic behavior of stochastic hyperbolic-parabolic equations with slow-fast time scales. Both the strong and weak convergence in the averaging principle are established. Then we study the stochastic fluctuations of the original system around its averaged equation. We show that the normalized difference converges weakly to the solution of a linear stochastic wave equation. An extra diffusion term appears in the limit which is given explicitly in terms of the solution of a Poisson equation. Furthermore, sharp rates for the above convergence are obtained, which are shown not to depend on the regularity of the coefficients in the equation for the fast variable.
Stichworte
Stochastic hyperbolic-parabolic equations;
Averaging principle;
Strong;
and weak convergence;
Homogenization
Erscheinungsjahr
2022
Zeitschriftentitel
Stochastics and Partial Differential Equations: Analysis and Computations
ISSN
2194-0401
eISSN
2194-041X
Page URI
https://pub.uni-bielefeld.de/record/2962448
Zitieren
Röckner M, Xie L, Yang L. Averaging principle and normal deviations for multi-scale stochastic hyperbolic-parabolic equations. Stochastics and Partial Differential Equations: Analysis and Computations . 2022.
Röckner, M., Xie, L., & Yang, L. (2022). Averaging principle and normal deviations for multi-scale stochastic hyperbolic-parabolic equations. Stochastics and Partial Differential Equations: Analysis and Computations . https://doi.org/10.1007/s40072-022-00248-8
Röckner, Michael, Xie, Longjie, and Yang, Li. 2022. “Averaging principle and normal deviations for multi-scale stochastic hyperbolic-parabolic equations”. Stochastics and Partial Differential Equations: Analysis and Computations .
Röckner, M., Xie, L., and Yang, L. (2022). Averaging principle and normal deviations for multi-scale stochastic hyperbolic-parabolic equations. Stochastics and Partial Differential Equations: Analysis and Computations .
Röckner, M., Xie, L., & Yang, L., 2022. Averaging principle and normal deviations for multi-scale stochastic hyperbolic-parabolic equations. Stochastics and Partial Differential Equations: Analysis and Computations .
M. Röckner, L. Xie, and L. Yang, “Averaging principle and normal deviations for multi-scale stochastic hyperbolic-parabolic equations”, Stochastics and Partial Differential Equations: Analysis and Computations , 2022.
Röckner, M., Xie, L., Yang, L.: Averaging principle and normal deviations for multi-scale stochastic hyperbolic-parabolic equations. Stochastics and Partial Differential Equations: Analysis and Computations . (2022).
Röckner, Michael, Xie, Longjie, and Yang, Li. “Averaging principle and normal deviations for multi-scale stochastic hyperbolic-parabolic equations”. Stochastics and Partial Differential Equations: Analysis and Computations (2022).
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