How can we reduce/simplify a huge Markov matrix?

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Muhammad Ali

I suggest you follow https://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter11.pdf

https://projecteuclid.org/euclid.bjps/1503388832

See also https://au.mathworks.com/matlabcentral/answers/57961-simulating-a-markov-chain

Qamar Abbas

yes, it is sparse but I cannot find any regular pattern of zeros.

Mohamed-Mourad Lafifi

Dear Qamar Abbas,

Please try using the Monte Carlo method and see this attached file, as an alternative i suggest you to take a look at links and attached file.

https://www.researchgate.net/publication/301249692_Simplification_of_irreversible_Markov_chains_by_removal_of_states_with_fast_leaving_rates

https://www.springer.com/gp/book/9783319779348

https://books.google.dz/books/about/Methods_and_Applications_of_Computationa.html?id=-eDMDwAAQBAJ&redir_esc=y

Best regards

Thanks for the answers.