Stochastic homeomorphism flows for SDEs driven by standard Brownian motion and fractional Brownian motion with non-Lipschitz coefficients

In this paper, under non-Lipschitz condition, we shall prove the homeomorphic flow property of solution to multidimensional stochastic differential equation (SDE) driven simultaneously by fractional Brownian motion with H ∈ ( 1 2 , 1 ) {H∈(1/2,1)} and standard Brownian motion.