Moment estimate and existence for the solution of neutral stochastic functional differential equation. (English) Zbl 1492.60160
Summary: In this paper, the existence and uniqueness for the global solution of neutral stochastic functional differential equation is investigated under the locally Lipschitz condition and the contractive condition. The implicit iterative methodology and the Lyapunov-Razumikhin theorem are used. The stability analysis for such equations is also applied. One numerical example is provided to illustrate the effectiveness of the theoretical results obtained.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H20 | Stochastic integral equations |
| 37H05 | General theory of random and stochastic dynamical systems |
| 37H20 | Bifurcation theory for random and stochastic dynamical systems |
Keywords:
neutral stochastic functional differential equation; existence and uniqueness; global solution; stabilityReferences:
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