Existence and Stability of Solutions to Highly Nonlinear Stochastic Differential Delay Equations Driven by G-Brownian Motion

2019 ◽  
Vol 34 (2) ◽  
pp. 184-204 ◽  
Author(s):  
Chen Fei ◽  
Wei-yin Fei ◽  
Li-tan Yan
Keyword(s):  
Brownian Motion ◽  
Delay Equations ◽  
Stability Of Solutions ◽  
Differential Delay ◽  
Differential Delay Equations ◽  
Stochastic Differential Delay Equations ◽  
Highly Nonlinear ◽  
Existence And Stability

scholarly journals Numerical method of highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuaibin Gao ◽  
Junhao Hu
Keyword(s):  
Numerical Solutions ◽  
Delay Equations ◽  
Markovian Switching ◽  
Type Condition ◽  
Differential Delay ◽  
Almost Sure Exponential Stability ◽  
Differential Delay Equations ◽  
Stochastic Differential Delay Equations ◽  
Highly Nonlinear ◽  
Strong Convergence Rate

AbstractIn this paper, we establish a partially truncated Euler–Maruyama scheme for highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching. We investigate the strong convergence rate and almost sure exponential stability of the numerical solutions under the generalized Khasminskii-type condition.

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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