# Markov n-step State Transition

I've understood the concept and application of the "recursive n-Step state transition formula" by Chapman/Kolmogorov. For those who don't recall it is this formula:

$$r_{ij}(n)=\sum_{k=1}^{m}r_{ik}(n-1)*p_{kj}$$

where
n= number of transitions
i= current node
j= destination node
m= number of nodes

I just wanted to know if there is a calculator, which lets me input everything and consequtively draws the graphs to n, calculates every matrix to n and also draws a timeline which includes the $p_{ij}$'s with increasing n?

I've been searching but could not find any program which does it alltogether.

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 Those are some very specific requirements. I'm not aware of any software that does all of them out of the box. I think you are going to have to either do some of the setup by hand, or write some code. – Nate Eldredge Feb 3 '12 at 12:38 seems so, i also couldnt find programs that satisfy those things – kiltek Feb 20 '12 at 6:02

I am not sure I understand all your notations, but denoting $R_n$ the matrix $R_n = \left[ r_{ij}(n) \right]_{ij}$ and $P$ the matrix $P = \left[ p_{ij} \right]_{ij}$, this formula seems to be just $$R_{n+1} = R_n \cdot P.$$ So the computation of $R_n$ is straightforward...