Uniformization

PSI is able to simulate continuous time model, but to realize this operation, we need to transform the generator matrix $\mathbf{Q}$ into an equivalent transition matrix $\mathbf{P}$.
That is $\mathbf{P}=I+\frac{1}{\Lambda_{max}}\mathbf{Q}$, where $\Lambda_{max}$ is the maximum of the absolute values of diagonal elements of $\mathbf{Q}$. This transformation [Ste94] permit to obtain a discrete time Markov chain verifying :

$$(\pi\mathbf{Q}=0 \Leftrightarrow \pi\mathbf{P}=\pi)$$