I haven't had much luck over in Stats SE, so I'm going to try over here.
I doubt many people here have experience with R, so I would like to know what are some methods to simulating a set of "nested" stochastic differential equations, i.e.,
$$\begin{align} &\dfrac{\text{d}S}{S}(t) = \alpha(t)\text{ d}t + \sigma(t)\text{ d}Z^{(1)}(t) \\ &\dfrac{\text{d}\sigma}{\sigma}(t) = \beta(t)\text{ d}t + \gamma(t)\text{ d}Z^{(2)}(t) \end{align}$$ where $Z^{(1)}$ and $Z^{(2)}$ are standard Brownian motions. Notice that $\sigma$ is used in both the SDE for $S$ and is given its own SDE as well. To keep this on-topic, I would like to emphasize that I'm looking for the math behind simulating these SDEs.
I figure by knowing these methods, I can at least try to figure out how to do what people suggest on R. Any pseudocode or code in Python (or similar languages) to supplement any mathematical discussion would be extremely helpful.