In this paper, we are concerned with a class of coupled multidimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter \(H\in (1/2,1)\). Using pathwise approach and based on Perov’s fixed point theorem, we prove that the existence and uniqueness of solution for the equations considered under some local Lipschitz conditions. Subsequently, by establishing some priori estimates, we obtain a viability result for the stochastic systems under investigation. The sufficient and necessary condition is also an alternative global existence result for the fractional differential equations with restrictions on the state. Finally, by direct and inverse images for fractional stochastic tangent sets, we establish the deterministic necessary and sufficient conditions which control that the solution for the coupled stochastic systems under investigation evolves in some particular sets.

在本文中，我们关注一类由Hurst参数\（H \ in（1 / 2,1）\）的分数布朗运动驱动的耦合多维随机微分方程。。使用路径方法并基于Perov不动点定理，我们证明了在某些局部Lipschitz条件下考虑的方程组解的存在性和唯一性。随后，通过建立一些先验估计，我们获得了所研究的随机系统的生存力结果。充分必要条件也是带状态约束的分数阶微分方程的替代全局存在结果。最后，通过分数随机切线集的正向和反向图像，我们确定了确定性的必要条件和充分条件，这些条件控制着耦合随机系统的解在某些特定集合中的演化。