Lorenz '96 system

\[dX_t = b_\theta(X_t)dt + \Sigma dW_t,\quad t\in[0,T],\quad X_0=x_0,\]

where $X$ and $W$ are d-dimensional, $\Sigma$ is a $d$ by $d$ diagonal matrix and $b$ is given by:

\[b^{[i]}_\theta(x):= (x^{[i+1]}-x^{[i-2]})x^{[i-1]}-x^{[i]}+\theta\]

where $i\in\{1,\dots,d\}$ is a cycling index.