Fixed points and stability of neutral stochastic delay differential equations

By Jiaowan Luo. 2007

110 citations recorded by the source corpus.

In this paper we consider a linear scalar neutral stochastic differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically mean square stable by means of fixed point theory. These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotic mean square stability theorem with a necessary and sufficient condition is proved. Some well-known results are improved and generalized.

Subfields: Applied Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f19c471c55672f7d03a0f3d396003e9ffc7c6f35

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Takeshi Taniguchi
2. Jiaowan Luo
3. Bixiang Wang
4. Kai Liu
5. Fulai Chen

In Control and Systems Engineering

1. Jiaowan Luo
2. Takeshi Taniguchi
3. Rathinasamy Sakthivel
4. Huabin Chen
5. Zuomao Yan
6. Kai Liu
7. Hongwu Zhang

In Numerical Analysis

1. Takeshi Taniguchi
2. Jiaowan Luo
3. Bixiang Wang
4. Fulai Chen

Citations in the corpus

• Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays (2008, unknown): “Luo [13] made the different method than in [1] to investigate the mean square asymptotical stability by means of fixed-point theory for stochastic delay differential equations, where the conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient function”
• Stability of stochastic partial differential equations with infinite delays (2008, methodology): “Very recently, Appleby [1] and Luo [11] have used the fixed point theory to deal with the stability for stochastic differential equations.”
• Fixed Points and Stability of Stochastic Neutral Partial Differential Equations with Infinite Delays (2009, methodology): “Luo, J. 2007.”