Mean-square asymptotic stability of the trivial solution of stochastic functional-differential equations

1980 ◽  
Vol 32 (1) ◽  
pp. 65-72 ◽  
Author(s):  
L. I. Yasinskaya ◽  
V. K. Yasinskii
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Trivial Solution ◽  
Functional Differential Equations ◽  
Mean Square ◽  
Stochastic Functional Differential Equations ◽  
Functional Differential ◽  
Stochastic Functional

scholarly journals The Almost Sure Asymptotic Stability and Boundedness of Stochastic Functional Differential Equations with Polynomial Growth Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Lichao Feng ◽  
Shoumei Li
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Growth Condition ◽  
Polynomial Growth ◽  
Linear Growth ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Linear Growth Condition ◽  
Functional Differential ◽  
Stochastic Functional

Stability and boundedness are two of the most important topics in the study of stochastic functional differential equations (SFDEs). This paper mainly discusses the almost sure asymptotic stability and the boundedness of nonlinear SFDEs satisfying the local Lipschitz condition but not the linear growth condition. Here we assume that the coefficients of SFDEs are polynomial or dominated by polynomial functions. We give sufficient criteria on the almost sure asymptotic stability and the boundedness for this kind of nonlinear SFDEs. Some nontrivial examples are provided to illustrate our results.

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