# American Institute of Mathematical Sciences

July  2019, 24(7): 3299-3318. doi: 10.3934/dcdsb.2018321

## Stochastic invariance for neutral functional differential equation with non-lipschitz coefficients

 Department of Probability and Statistics, School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, MO 510006, China

* Corresponding author: Jiaowan Luo

Received  February 2018 Revised  July 2018 Published  January 2019

Fund Project: The second author is supported by NNSF grant 11271093.

In this paper, by the use of martingale property and spectral decomposition theory, we investigate the stochastic invariance for neutral stochastic functional differential equations (NSFDEs) and provide necessary and sufficient conditions for the invariance of closed sets of $R^{d}$ with non-Lipschitz coefficients. A pathwise asymptotic estimate example is given to illustrate the feasibility and effectiveness of obtained result.

Citation: Chunhong Li, Jiaowan Luo. Stochastic invariance for neutral functional differential equation with non-lipschitz coefficients. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3299-3318. doi: 10.3934/dcdsb.2018321
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