define $A$ (since the effective rate of exit out of $A$ must be the unbiased statistical steady one) and by $\nu_{\alpha,\beta}^A=0$ if $\alpha$ is the index of a cell $B_\alpha$ used to define $B$ (since the effective rate of exit out of $B$ must be zero). We also set $\pi^A_\alpha=\pi_\alpha$ if $\alpha$ is the index of a cell $B_\alpha$ used to define $A$, $\pi^A_\alpha=0$ if $\alpha$ is the index of a cell $B_\alpha$ used to define $B$, and in all the other cells we compute $\pi^A_\alpha$ via $$\label{eq:peqA}
  \sum_{\substack{\beta=1\\ \beta \not=\alpha}
  }^{\Lambda} \pi^A_{\beta} \nu^A_{\beta,\alpha} = 
  \sum_{\substack{\beta=1\\ \beta \not=\alpha}}^{\Lambda} 
  \pi^A_{\alpha} \nu^A_{\alpha,\beta}$$ where the index $\alpha$ runs over all the cells outside of $A$ and $B$ and we use as boundary conditions the values for $\nu_{\beta,\alpha}^A$ and $\pi^A_\beta$ set before when the index $\beta$ is that of a cell used to define $A$ or $B$. Finally, we compute the probability of re-entry on the edges of a cell $B_\alpha$ not inside $A$ and $B$ as $$\label{eq:probfluxA}
  \PP^A_{\partial B_{\beta} \cap \partial B_{\alpha}}=
  \frac{\pi^A_{\beta} \nu^A_{\beta,\alpha}}
  {\sum_{\beta'\neq\alpha} \pi^A_{\beta'} \nu^A_{\beta',\alpha} }, 
  \quad (\beta\neq \alpha).$$ This procedure automatically guarantees that we focus on the trajectories assigned to $A$ and makes all the quantities above – the set 