A NEW LaSalle-TYPE THEOREM FOR STOCHASTIC DIFFERENTIAL DELAY EQUATIONS OF NEUTRAL TYPE

2007 ◽  
Vol 07 (04) ◽  
pp. 459-478
Author(s):  
WEIXING DAI ◽  
SHIGENG HU
Keyword(s):  
Asymptotic Stability ◽  
Type Theorem ◽  
Neutral Type ◽  
Delay Equations ◽  
Differential Delay ◽  
Differential Delay Equations ◽  
Stochastic Differential Delay Equations

The main aim of this paper is to establish a new LaSalle-type theorem for stochastic differential delay equations of neutral type. From the theorem follow some useful criteria on the orbital asymptotic stability. Several examples are also given for illustration. This shows clearly the power of our new theorem.

On the Partial Stochastic Stability of Stochastic Differential Delay Equations with Markovian Switching

2013 ◽  
Vol 765-767 ◽  
pp. 709-712 ◽  
Author(s):  
De Zhi Liu ◽  
Wei Qun Wang
Keyword(s):  
Asymptotic Stability ◽  
Stochastic Stability ◽  
Sufficient Conditions ◽  
Delay Equations ◽  
Markovian Switching ◽  
Differential Delay ◽  
Stability In Probability ◽  
Differential Delay Equations ◽  
Stochastic Differential Delay Equations ◽  
Asymptotic Stability In Probability

In the paper, we are concerned with the partial asymptotic stochastic stability (stability in probability) of stochastic differential delay equations with Markovian switching (SDDEwMSs), the sufficient conditions for partial asymptotic stability in probability have been given and we have generalized some results of Sharov and Ignatyev to cover a class of much more general SDDEwMSs.

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