We call $W_{ij}$ for the transition probability and we represent it as a matrix.

• Both $W$ and $w$ represent probabilities and they have to be normalized, meaning that at each time step we have

$$\begin{equation*} \sum_i w_i(t) = 1, \end{equation*}$$ and $$\begin{equation*} \sum_j W(j\rightarrow i) = 1. \end{equation*}$$ Here we have written the previous matrix $W_{ij}=W(j\rightarrow i)$.