With Mathematica 9, we have the addition of various processes, among which the discrete Markov process. Given a transition probability matrix m
, such a process is defined as follows:
m = {{1/4, 1/4, 1/4, 1/4, 0, 0},
{1/3, 0, 1/3, 1/3, 0, 0},
{0, 1/2, 0, 1/4, 1/16, 3/16},
{0, 0, 0, 1/2, 1/2, 0},
{0, 0, 0, 0, 1/2, 1/2},
{0, 0, 0, 0, 0, 1}
};
proc = DiscreteMarkovProcess[1, m];
g1 = Graph[proc]
Various properties of a given Markov process can be found using the function MarkovProcessProperties
. Probability
can be used (among other things) to answer questions about the likelihood to end up in a certain state after a given number of steps.
However, I did not find a function that yields the path that is most likely to be taken between a given a starting and ending state. How would one find this path?