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 Jan 9 awarded Scholar Jan 9 accepted Proof about Steady-State distribution of a Markov chain Jan 9 comment Multi-variate monotonic function Right. I totally missed that. So I can get rid of the $\pi_\delta(j)$ on the right-hand side. But is it enough to show that the derivative does not change sign? Jan 9 asked Multi-variate monotonic function Jan 4 comment Proof about Steady-State distribution of a Markov chain OK, now I understand everything you have written. Can I now get the monotonicity per position in distribution (for instance for $i$-th element), if I rewrite the formula for index $i$? Instead of $\nu_\delta$ I would look at $\nu_\delta(i)$. Jan 4 awarded Supporter Jan 4 comment Proof about Steady-State distribution of a Markov chain I suppose you meant $K_\delta$ instead of $N_\delta$... Anyway, i do not understand what you meant by $\sum \nu_\delta = 0$. Isn't $\nu_\delta$ fixed for some $\delta$. How can we sum them? Jan 3 awarded Editor Jan 3 comment Proof about Steady-State distribution of a Markov chain @Ilya I edited the question. Jan 3 revised Proof about Steady-State distribution of a Markov chain added 914 characters in body Jan 3 comment Proof about Steady-State distribution of a Markov chain I found the problem. We do not start with a matrix that represents a Markov chain, but we start with some fixed matrix. Then we add the $\delta$ on the diagonal and then normalize the rows. Sorry for the mistake. I will edit the question. Jan 3 comment Proof about Steady-State distribution of a Markov chain Wow... there is something definetely wrong (on my part). I have to check, where did I go wrong. Jan 3 comment Proof about Steady-State distribution of a Markov chain @Ilya so if I understand you correctly, you are saying that $\pi=\pi_\delta$ for all $\delta<\infty$? Jan 3 awarded Student Jan 3 comment Proof about Steady-State distribution of a Markov chain Yes it is not compatible. In my method I am using $0< \delta \leq 1$, but I noticed that if I increase $\delta$ to some larger values (e. g. 100), the values converge to above mentioned $\pi_C$ and not to $[0.25,0.25,0.25,0.25]$. Sorry for the confusion, I am a decision support grad students and mathematics was just a part of my undergrad program. Jan 3 asked Proof about Steady-State distribution of a Markov chain Sep 26 awarded Autobiographer