I don't understand what you are proving. By definition of time-homogeneity for DTMCs, the probability of the process of passing from one state i at time time n to another state j at time n+1 is independent of the particular time n. Thus, this also holds when you are considering the process at the stopping time.
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Thanks PROF 👍
@armanavagyan1876 Markov Chains are so cool!
I don't understand what you are proving.
By definition of time-homogeneity for DTMCs, the probability of the process of passing from one state i at time time n to another state j at time n+1 is independent of the particular time n.
Thus, this also holds when you are considering the process at the stopping time.