In Itô calculus, it is easy to construct an associativity rule. Namely, if $B_t$ is a Brownian motion and $M_t = \int_0^t X_s dB_s$ for suitable $X_t$, then we have the following associativity rule: $Z_t = \int_0^t Y_s dM_s = \int_0^t Y_s X_s dB_s$. Such a rule can be derived by defining a martingale calculus, or more generally can be extracted from semimartingale calculus.

Is it possible to obtain a similar expression when the integrator $B_t$ is replaced by $B_t^{(H)}$, a fractional Brownian motion with Hurst index $H \neq \frac{1}{2}$? In this setting, one can't pass through a semimartingale calculus as $B_t^{(H)}$ is no longer a semimartingale. My feeling is that the answer may depend on the choice of $H$, as this affects the construction of the integral.