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Heston model is described by following SDE \begin{equation} \begin{aligned} dS_t &= \mu S_t dt + \sqrt{\nu_t} S_t dW^S_t \\ d\nu_t &= \kappa(\theta - \nu_t) dt + \xi \sqrt{\nu_t} dW^{\nu}_t \\ \textrm{Corr}[W^S_t, W^{\nu}_t] &= \rho \end{aligned} \end{equation}

If I use Milstein scheme for $\nu _t$ and $S_t$, what will be the rate of convergence of process $S$ (when I compare results with denser mesh)? Is it $1.0$ or no?

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