Comparison principle and stability of Ito stochastic differential delay equations with Poisson jump and Markovian switching

2006 ◽  
Vol 64 (2) ◽  
pp. 253-262 ◽  
Author(s):  
Jiaowan Luo
Keyword(s):  
Comparison Principle ◽  
Delay Equations ◽  
Markovian Switching ◽  
Differential Delay ◽  
Differential Delay Equations ◽  
Stochastic Differential Delay Equations ◽  
Poisson Jump

scholarly journals Analytic Approximation of the Solutions of Stochastic Differential Delay Equations with Poisson Jump and Markovian Switching

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hua Yang ◽  
Feng Jiang
Keyword(s):  
Diffusion Coefficients ◽  
Numerical Solutions ◽  
Delay Equations ◽  
Markovian Switching ◽  
Analytic Approximation ◽  
Differential Delay ◽  
Differential Delay Equations ◽  
Stochastic Differential Delay Equations ◽  
Poisson Jump ◽  
And Diffusion

We are concerned with the stochastic differential delay equations with Poisson jump and Markovian switching (SDDEsPJMSs). Most SDDEsPJMSs cannot be solved explicitly as stochastic differential equations. Therefore, numerical solutions have become an important issue in the study of SDDEsPJMSs. The key contribution of this paper is to investigate the strong convergence between the true solutions and the numerical solutions to SDDEsPJMSs when the drift and diffusion coefficients are Taylor approximations.

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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