scholarly journals Averaging Principle and Normal Deviations for Multiscale Stochastic Systems

2021 ◽  
Vol 383 (3) ◽  
pp. 1889-1937
Author(s):  
Michael Röckner ◽  
Longjie Xie
Keyword(s):  
Stochastic Systems ◽  
Averaging Principle

scholarly journals The Averaging Principle for Stochastic Pantograph Equations with Non-Lipschitz Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Dongdong Gao ◽  
Jianli Li ◽  
Zhiguo Luo ◽  
Danfeng Luo
Keyword(s):  
Stochastic Systems ◽  
Averaging Principle ◽  
Mean Square ◽  
The Mean ◽  
Lipschitz Conditions

This paper is devoted to presenting an averaging principle for stochastic pantograph equations. Under suitable non-Lipschitz conditions, the solutions to stochastic pantograph equations can be approximated by solutions to averaged stochastic systems in the mean-square sense and probability. At last, an example is given to demonstrate the feasibility of obtained results. Moreover, our results have generalized significantly some previous ones.

scholarly journals Averaging Principle for Backward Stochastic Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yuanyuan Jing ◽  
Zhi Li
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Systems ◽  
Backward Stochastic Differential Equations ◽  
Averaging Principle ◽  
Mean Square ◽  
The One

The averaging principle for BSDEs and one-barrier RBSDEs, with Lipschitz coefficients, is investigated. An averaged BSDEs for the original BSDEs is proposed, as well as the one-barrier RBSDEs, and their solutions are quantitatively compared. Under some appropriate assumptions, the solutions to original systems can be approximated by the solutions to averaged stochastic systems in the sense of mean square.

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