[markov_chains] Integrate Comments

[HumphreyYang]

Similar to the LLN and CLT lecture, this PR resolves some of the comments proposed this morning. Due to the audio quality, I missed some of the valuable comments from the team. Please kindly comment on this PR so that I can further improve this lecture.

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[HumphreyYang]

@mmcky there seem to be false positives in the line checker:

https://stats.libretexts.org/Bookshelves/Probability_Theory/Probability_Mathematical_Statistics_and_Stochastic_Processes_(Siegrist)/16:_Markov_Processes/16.05:_Periodicity_of_Discrete-Time_Chains#:~:text=A%20state%20in%20a%20discrete,limiting%20behavior%20of%20the%20chain. - Anchor ':~:text=A%20state%20in%20a%20discrete,limiting%20behavior%20of%20the%20chain.' not found

zreferences: line   13) broken    https://doi.org/10.1257/aer.20151684 - 403 Client Error: Forbidden for url: https://pubs.aeaweb.org/doi/10.1257/aer.20151684

Many thanks if you could take a look :)

[jstac]

Thanks @HumphreyYang , it's looking good. Small comments above.

[mmcky]

thanks @HumphreyYang would you mind to review the merge conflict? It looks like there have been updates made on the main branch.

[HumphreyYang]

thanks @HumphreyYang would you mind to review the merge conflict? It looks like there have been updates made on the main branch.

Many thanks! It seems like the main branch has some building issues.

[jstac]

Thanks @HumphreyYang .

@mmcky , please merge when ready (noting the build failure).

[jstac]

@mmcky I couldn't see what the build issue was but I'm going to go ahead and merge this. We can iterate from there.