Stochastic invariance for neutral functional differential equation with non-Lipschitz coefficients. (English) Zbl 1415.60084
Summary: 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.
MSC:
60H30 | Applications of stochastic analysis (to PDEs, etc.) |
60H25 | Random operators and equations (aspects of stochastic analysis) |
65C30 | Numerical solutions to stochastic differential and integral equations |