Long time behavior of stochastic differential equations driven by linear multiplicative fractional noise.

We consider the (rough) stochastic differential equations driven by a linear multiplicative fractional Brownian motion with Hurst index H ∈ (1 2 , 1) (or a linear multiplicative geometric fractional Brownian rough path with Hurst index H ∈ (1 3 , 1 2 ]), we construct the pullback random attractors for these two type noises via the transformation method. Furthermore, we obtain the invariant probability measures, which are supported on the pullback random attractors. Finally, we obtain the limit behavior of the invariant probability measures. [ABSTRACT FROM AUTHOR]