### Averaging Principle and Normal Deviations for Multiscale Stochastic Systems

Röckner M, Xie L (2021)
Communications in Mathematical Physics 383(3): 1889–1937.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Röckner, MichaelUniBi; Xie, Longjie
Einrichtung
Abstract / Bemerkung
We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle of functional law of large numbers type are established. Then we consider the small fluctuations of the system around its average. Nine cases of functional central limit type theorems are obtained. In particular, even though the averaged equation for the original system is the same, the corresponding homogenization limit for the normal deviation can be quite different due to the difference in the interactions between the fast scales and the deviation scales. We provide quite intuitive explanations for each case. Furthermore, sharp rates both for the strong convergences and the functional central limit theorems are obtained, and these convergences are shown to rely only on the regularity of the coefficients of the system with respect to the slow variable, and do not depend on their regularity with respect to the fast variable, which coincide with the intuition since in the limit equations the fast component has been totally averaged or homogenized out.
Erscheinungsjahr
2021
Zeitschriftentitel
Communications in Mathematical Physics
Band
383
Ausgabe
3
Seite(n)
1889–1937
ISSN
0010-3616
eISSN
1432-0916
Page URI
https://pub.uni-bielefeld.de/record/2954682

### Zitieren

Röckner M, Xie L. Averaging Principle and Normal Deviations for Multiscale Stochastic Systems. Communications in Mathematical Physics. 2021;383(3):1889–1937.
Röckner, M., & Xie, L. (2021). Averaging Principle and Normal Deviations for Multiscale Stochastic Systems. Communications in Mathematical Physics, 383(3), 1889–1937. https://doi.org/10.1007/s00220-021-04069-z
Röckner, M., and Xie, L. (2021). Averaging Principle and Normal Deviations for Multiscale Stochastic Systems. Communications in Mathematical Physics 383, 1889–1937.
Röckner, M., & Xie, L., 2021. Averaging Principle and Normal Deviations for Multiscale Stochastic Systems. Communications in Mathematical Physics, 383(3), p 1889–1937.
M. Röckner and L. Xie, “Averaging Principle and Normal Deviations for Multiscale Stochastic Systems”, Communications in Mathematical Physics, vol. 383, 2021, pp. 1889–1937.
Röckner, M., Xie, L.: Averaging Principle and Normal Deviations for Multiscale Stochastic Systems. Communications in Mathematical Physics. 383, 1889–1937 (2021).
Röckner, Michael, and Xie, Longjie. “Averaging Principle and Normal Deviations for Multiscale Stochastic Systems”. Communications in Mathematical Physics 383.3 (2021): 1889–1937.

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