If $M$ is a row-normalised Markov matrix, $I$ is an identity matrix, $P=\text{diag}([p_1,\cdots,p_n])$ is a diag matrix and satisfies $p_i\in(0,1)$. When $t\rightarrow \infty$, what is the convergence limit of $I + PM + P^2M^2 + \cdots + P^tM^t + \cdots$?
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This question is similar with the question "https://math.stackexchange.com/questions/21055/a-geometric-infinite-sum-of-matrices" – Jonway Feb 08 '22 at 07:46
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and the question "https://math.stackexchange.com/questions/2854333/a-geometric-ish-infinite-sum-of-matrices?noredirect=1&lq=1" – Jonway Feb 08 '22 at 07:57