TY - JOUR
T1 - Averaging principles formixed fast-slow systems driven by fractional Brownian motion
AU - Pei, Bin
AU - Inahama, Yuzuru
AU - Xu, Yong
N1 - Publisher Copyright:
© 2023 by Kyoto University.
PY - 2023
Y1 - 2023
N2 - We focus on fast-slow systems involving both fractional Brownian motion (fBm) and standard Brownian motion (Bm). The integral with respect to Bm is the standard Itô integral, and the integral with respect to fBm is a generalized Riemann- Stieltjes integral by means of fractional calculus.We establish an averaging principle in which the fast-varying diffusion process of the fast-slow systems acts as a "noise"to be averaged out in the limit.We show that the slow process has a limit in the mean square sense, which is characterized by the solution of stochastic differential equations driven by fBm whose coefficients are averaged with respect to the stationary measure of the fast-varying diffusion. An implication is that one can ignore the complex original systems and concentrate on the averaged systems instead. This averaging principle paves the way for reduction of computational complexity.
AB - We focus on fast-slow systems involving both fractional Brownian motion (fBm) and standard Brownian motion (Bm). The integral with respect to Bm is the standard Itô integral, and the integral with respect to fBm is a generalized Riemann- Stieltjes integral by means of fractional calculus.We establish an averaging principle in which the fast-varying diffusion process of the fast-slow systems acts as a "noise"to be averaged out in the limit.We show that the slow process has a limit in the mean square sense, which is characterized by the solution of stochastic differential equations driven by fBm whose coefficients are averaged with respect to the stationary measure of the fast-varying diffusion. An implication is that one can ignore the complex original systems and concentrate on the averaged systems instead. This averaging principle paves the way for reduction of computational complexity.
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U2 - 10.1215/21562261-2023-0001
DO - 10.1215/21562261-2023-0001
M3 - Article
AN - SCOPUS:85150661387
SN - 2156-2261
VL - 63
SP - 721
EP - 748
JO - Kyoto Journal of Mathematics
JF - Kyoto Journal of Mathematics
IS - 4
ER -