TY - JOUR
T1 - Moderate Deviations for Two-Time Scale Systems with Mixed Fractional Brownian Motion
AU - Yang, Xiaoyu
AU - Inahama, Yuzuru
AU - Xu, Yong
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
PY - 2024/8
Y1 - 2024/8
N2 - This work focuses on moderate deviations for two-time scale systems with mixed fractional Brownian motion. Our proof uses the weak convergence method which is based on the variational representation formula for mixed fractional Brownian motion. Throughout this paper, the Hurst parameter of fractional Brownian motion is larger than 1/2 and the integral along the fractional Brownian motion is understood as the generalized Riemann-Stieltjes integral. First, we consider single-time scale systems with fractional Brownian motion. The key of our proof is showing the weak convergence of the controlled system. Next, we extend our method to show moderate deviations for two-time scale systems. To this goal, we combine the Khasminskii-type averaging principle and the weak convergence approach.
AB - This work focuses on moderate deviations for two-time scale systems with mixed fractional Brownian motion. Our proof uses the weak convergence method which is based on the variational representation formula for mixed fractional Brownian motion. Throughout this paper, the Hurst parameter of fractional Brownian motion is larger than 1/2 and the integral along the fractional Brownian motion is understood as the generalized Riemann-Stieltjes integral. First, we consider single-time scale systems with fractional Brownian motion. The key of our proof is showing the weak convergence of the controlled system. Next, we extend our method to show moderate deviations for two-time scale systems. To this goal, we combine the Khasminskii-type averaging principle and the weak convergence approach.
KW - 60F10
KW - 60G15
KW - 60H10
KW - Fractional Brownian motion
KW - Moderate deviation
KW - Two-time scale system
KW - Weak convergence method
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U2 - 10.1007/s00245-024-10159-w
DO - 10.1007/s00245-024-10159-w
M3 - Article
AN - SCOPUS:85197729320
SN - 0095-4616
VL - 90
JO - Applied Mathematics and Optimization
JF - Applied Mathematics and Optimization
IS - 1
M1 - 18
ER -