Markov Chains: n-step Transition Matrix | Part - 3

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Let's understand Markov chains and its properties. In this video, I've discussed the higher-order transition matrix and how they are related to the equilibrium state.
#markovchain #datascience #statistics

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Teamsoakbeans

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These animation combined videos just make you understand 30 mins topic in 10 mins.

Garrick

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tasnimmeem

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ericrogers

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Thanks!

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soumodeepsen

Notes for my future review.

05:06
*Chanpman-Kolmogorov Theorem*
can be used to calculate the probability of going from state i to state j after n steps.

05:06 = Probability of going from state i to state j in n steps with an intermiadte stop in state k after r steps, then sum over all possible value of k.

Probability for going from state i to state j after n step
= Probililty of going from state i into a in-between state * Probability of going from the in-between states to j state, for all the possible in-between state
= ( Proability of going from state i to k after r steps * Probaility of going from k to n after n-r steps ).sum_for_all_k_states

In other words: Get the probability of going from state-i to state-j in n step, through a state k. Do it for all possible state k. Then sum all the probabilities.
But what is r? What is the value of r?

The system reaches an intermidiate state k after r steps. There are different possible k states, so for each k, the r (the number of step to reach from i to k) might be different.

The exact value of r is not important, except that probability of k to j is for n-r steps.

karannchew

Thank you so much for the videos. You explained Markov Chain a lot better than my professor. You have mentioned aperiodicity in this video but you have not talked about it in later videos.

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daniel__

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saeedeh_nikan

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