A note on exponential stability of non-autonomous linear stochastic differential delay equations driven by a fractional Brownian motion with Hurst index>12

2018 ◽  
Vol 138 ◽  
pp. 127-136 ◽  
Author(s):  
Phan Thanh Hong ◽  
Cao Tan Binh
Keyword(s):  
Brownian Motion ◽  
Exponential Stability ◽  
Fractional Brownian Motion ◽  
Delay Equations ◽  
Hurst Index ◽  
Differential Delay ◽  
Differential Delay Equations ◽  
Stochastic Differential Delay Equations

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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