# mixing fractional Brownian motions

Given two Brownian motions $$W_t^1, W_t^2$$, we can have them correlated by $$W_t^1 = \rho W_t^2+\sqrt{1-\rho^2}Z_t$$ where $$W_t^{2}$$ and $$Z_t$$ are independent of each other.

My question then: is there any similar relationship between fractional Brownian motions? In other words, given $$W_t^{H_2}, Z_t^{H_3}$$ two independent fractional Bm, can we say anything about $$\rho W_t^{H_2}+\sqrt{1-\rho^2}Z_t$$ or $$\rho W_t^{H_2}+\sqrt{1-\rho^2}Z_t^{H_3}$$ for $$H_2$$ and $$H_3$$ not necessarily equal? Can they generate a new correlated fBm $$W_t^{H_1}$$?