Diffusion approximation for fully coupled stochastic differential equations

Röckner M, Xie L (2021)
Annals of Probability 49(3): 1205-1236.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Röckner, MichaelUniBi; Xie, Longjie
Abstract / Bemerkung
We consider a Poisson equation in R-d for the elliptic operator corresponding to an ergodic diffusion process. Optimal regularity and smoothness with respect to the parameter are obtained under mild conditions on the coefficients. The result is then applied to establish a general diffusion approximation for fully coupled multitime scales stochastic differential equations with only Holder continuous coefficients. Four different averaged equations as well as rates of convergence are obtained. Moreover, the convergence is shown to rely only on the regularities of the coefficients with respect to the slow variable and does not depend on their regularities with respect to the fast component.
Stichworte
Poisson equation; multiscale system; averaging principle; diffusion; approximation; homogenization
Erscheinungsjahr
2021
Zeitschriftentitel
Annals of Probability
Band
49
Ausgabe
3
Seite(n)
1205-1236
ISSN
0091-1798
Page URI
https://pub.uni-bielefeld.de/record/2955367

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Röckner M, Xie L. Diffusion approximation for fully coupled stochastic differential equations. Annals of Probability. 2021;49(3):1205-1236.
Röckner, M., & Xie, L. (2021). Diffusion approximation for fully coupled stochastic differential equations. Annals of Probability, 49(3), 1205-1236. https://doi.org/10.1214/20-AOP1475
Röckner, M., and Xie, L. (2021). Diffusion approximation for fully coupled stochastic differential equations. Annals of Probability 49, 1205-1236.
Röckner, M., & Xie, L., 2021. Diffusion approximation for fully coupled stochastic differential equations. Annals of Probability, 49(3), p 1205-1236.
M. Röckner and L. Xie, “Diffusion approximation for fully coupled stochastic differential equations”, Annals of Probability, vol. 49, 2021, pp. 1205-1236.
Röckner, M., Xie, L.: Diffusion approximation for fully coupled stochastic differential equations. Annals of Probability. 49, 1205-1236 (2021).
Röckner, Michael, and Xie, Longjie. “Diffusion approximation for fully coupled stochastic differential equations”. Annals of Probability 49.3 (2021): 1205-1236.

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