# Markov Chain w/ non-stochastic matrix

I've come across a problem which at first appeared to be a markov process however the transition matrix of the graph is non-stochastic. That is, the probabilities among edges leaving a node do not sum to 1. However,the probabilities on edges entering the node do sum to 1. Therefore the transpose of the transition matrix IS stochastic.

I've built up a model in excel and noticed a few properties of this "transpose markovian process":

1. all nodes reach the same steady state value.
2. the steady state *is* dependent on the initial state (unlike a markov process).
3. the steady state value can be computed as S0 x MT (the initial state vector times the transpose of the markovian steady state vector... obtained by transposing the transition matrix and solving as a markov process).

My question is this: Is there a name for such a process? In searching for it I've found it to be beyond obscure, so my hope is some well-informed human can catalyze me with some search terms.

• This is a nice question, but also a pure mathematics question. Should we migrate to Mathematics? – Raphael Mar 16 '15 at 7:31
• "Is there a name for X?" is typically not an ideal question. If the answer is "No", how do you plan to evaluate the answer? Instead, I suggest that you first figure out why you are hoping to find a name (what will you do it? what is the real problem you are trying to solve?), and then ask about that -- ask about the real problem that you are trying to solve. Even if someone told you a name, that'd be only a means to an end -- so what's the end that you're striving for? If you're looking for literature about this processes, what questions specifically are you hoping it would answer? – D.W. Mar 16 '15 at 7:32