# 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

## 1 Answer

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...

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 no i know how to calculate using the formula. i'm just asking for the program described in the second paragraph of my post. – kiltek Jan 3 '12 at 11:55 @kiltek Do you use R ? – Elvis Jan 3 '12 at 12:00 With "R" i could write it myself. I need a ready program. – kiltek Jan 3 '12 at 12:03 @kiltek That's not what I'm asking. Would a R script satisfy you? – Elvis Jan 3 '12 at 12:30 Of course, if it does the following: -ask for number of nodes beginning matrix, ask for number of transitions on beginning graph, draw graphs from beginning matix to number of transitions, draw matrices from beginning matrix to number of transisitons, draw timelines from beginning matrix to number of transisitons matrix, (with timeline i mean a graph, that has a x-Axis with increasing number of transitions and an y-Axis with the corresponding probabilities, for each \$r_{ij}), thats a lot of requirements, thats why im asking for a ready program, best found by google for free – kiltek Jan 3 '12 at 13:24