Two-time-scale stochastic differential delay equations driven by multiplicative fractional Brownian noise: Averaging principle

2022 ◽  
pp. 126004
Author(s):  
Min Han ◽  
Yong Xu ◽  
Bin Pei ◽  
Jiang-Lun Wu
Keyword(s):  
Time Scale ◽  
Delay Equations ◽  
Averaging Principle ◽  
Differential Delay ◽  
Differential Delay Equations ◽  
Stochastic Differential Delay Equations ◽  
Brownian Noise ◽  
Fractional Brownian Noise

scholarly journals An Averaging Principle for Stochastic Differential Delay Equations with Fractional Brownian Motion

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Yong Xu ◽  
Bin Pei ◽  
Yongge Li
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Path Integrals ◽  
Delay Equations ◽  
Averaging Principle ◽  
Stochastic Integration ◽  
Differential Delay ◽  
Differential Delay Equations ◽  
Stochastic Differential Delay Equations ◽  
Convergence In Mean

An averaging principle for a class of stochastic differential delay equations (SDDEs) driven by fractional Brownian motion (fBm) with Hurst parameter in(1/2,1)is considered, where stochastic integration is convolved as the path integrals. The solutions to the original SDDEs can be approximated by solutions to the corresponding averaged SDDEs in the sense of both convergence in mean square and in probability, respectively. Two examples are carried out to illustrate the proposed averaging principle.

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