Announcements

Hello,

I realize that a notation in HW4 might not be crystal clear to you. This notation "will be" explained only in Lecture 5 (the thing is, I prepared Lecture 5 a month ago: this is one of the disadvantages of these prerecorded classes: you lose track of what you already said while preparing  exercises...).

The notation in question is $\Vert P_i^{n} - \pi \Vert_{\mathrm{TV}}$. Here, $P_i^n$ stands actually for the $i$-th row of the matrix $P^n$: it is the distribution $\pi^{(n)}$ of the Markov chain at time $n$, given that the chain started in state $i$ at time 0 (i.e. $\pi^{(0)}=\delta_i$).

So to be clear: $\Vert P_i^{n} - \pi \Vert_{\mathrm{TV}} = \frac{1}{2} \sum_{j \in {\mathcal S}} |p_{ij}(n)-\pi_j|$

All the best,

Olivier