Averaging principles formixed fast-slow systems driven by fractional Brownian motion

Bin Pei, Yuzuru Inahama, Yong Xu

研究成果: ジャーナルへの寄稿学術誌査読

4 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)721-748
ページ数28
ジャーナルKyoto Journal of Mathematics
63
4
DOI
出版ステータス出版済み - 2023

!!!All Science Journal Classification (ASJC) codes

  • 数学一般

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