Stationary probability in Markov

[mertcan]

Hi, initially you can examine in the attachment that when we multiply transition infinitely we have same rows, and we called them $$\pi$$ but without trying multiple times how do we know that this matrix converge ? Is there derivation of this ?? I really tried to find the some proofs but the only thing I found is this proof was made by Wolfgang Doeblin...

 

[mertcan]

@Ray Vickson I will be also waiting for your valuable returns...