# Solving chemical master equation using Kolmogorov system

I am recently studying about chemical reaction networks. And I have problem about application of Kolmogorov system to actual examples.

So, here's a chemical reaction

$$S_1 + S_2 \rightarrow S_3$$ with $$k_1$$.

$$S_3 \rightarrow S_1 + S_2$$ with $$k_2$$.

So, I know that propensity functions are $$k_1 N_1 N_2$$ and $$k_2 N_3$$. But how can I get the mean and variance of $$S_1$$ from Kolmogorov system? I studied the concept of Kolmogorov system, but I still have no idea how to get it.

And here's the paper : https://aip.scitation.org/doi/10.1063/1.3103264