Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations

Röckner M, Sun X, Xie Y (2021)
Annales de l'Institut Henri Poincaré (B): Probability and Statistics 57(1): 547-576.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Röckner, MichaelUniBi; Sun, Xiaobin; Xie, Yingchao
Abstract / Bemerkung
In this paper, we consider the averaging principle for a class of McKean-Vlasov stochastic differential equations with slow and fast time-scales. Under some proper assumptions on the coefficients, we first prove that the slow component strongly converges to the solution of the corresponding averaged equation with convergence order 1/3 using the approach of time discretization. Furthermore, under stronger regularity conditions on the coefficients, we use the technique of Poisson equation to improve the order to 1/2, which is the optimal order of strong convergence in general.
Stichworte
Averaging principle; McKean-Vlasov stochastic differential equations; Slow-fast; Poisson equation; Strong convergence order
Erscheinungsjahr
2021
Zeitschriftentitel
Annales de l'Institut Henri Poincaré (B): Probability and Statistics
Band
57
Ausgabe
1
Seite(n)
547-576
ISSN
0246-0203
Page URI
https://pub.uni-bielefeld.de/record/2953834

Zitieren

Röckner M, Sun X, Xie Y. Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations. Annales de l'Institut Henri Poincaré (B): Probability and Statistics. 2021;57(1):547-576.
Röckner, M., Sun, X., & Xie, Y. (2021). Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations. Annales de l'Institut Henri Poincaré (B): Probability and Statistics, 57(1), 547-576. https://doi.org/10.1214/20-AIHP1087
Röckner, M., Sun, X., and Xie, Y. (2021). Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations. Annales de l'Institut Henri Poincaré (B): Probability and Statistics 57, 547-576.
Röckner, M., Sun, X., & Xie, Y., 2021. Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations. Annales de l'Institut Henri Poincaré (B): Probability and Statistics, 57(1), p 547-576.
M. Röckner, X. Sun, and Y. Xie, “Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations”, Annales de l'Institut Henri Poincaré (B): Probability and Statistics, vol. 57, 2021, pp. 547-576.
Röckner, M., Sun, X., Xie, Y.: Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations. Annales de l'Institut Henri Poincaré (B): Probability and Statistics. 57, 547-576 (2021).
Röckner, Michael, Sun, Xiaobin, and Xie, Yingchao. “Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations”. Annales de l'Institut Henri Poincaré (B): Probability and Statistics 57.1 (2021): 547-576.

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