Is it possible to translate a small system of ODEs to a discrete stochastic model? If so, can someone show me how?
I am trying to obtain the transition rate equations of the continuous time markov chain and then construct the infinitesimal generator matrix.
Equations: $$ \frac{dx}{dt} = Q_x-\lambda_x \cdot x - \beta_x \cdot x \cdot z \\ \frac{dy}{dt} = Q_y -\lambda_y \cdot y - \beta_y \cdot y \cdot z \\ \frac{dz}{dt} = Q_z - \lambda_z \cdot z - \frac{\beta_z}{n} \cdot y \cdot z $$
where the $Q$'s, $\lambda$'s, and $\beta$'s are parameters in $\mathbb{R}^{+}$ and $n$ takes on positive integer values.
Thanks in advance for any help.