123 reputation
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bio website d-sajt.com
location Slovenia
age 26
visits member for 1 year, 10 months
seen Jun 26 at 12:32

Something.


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