Algorithms for determining the transient and differential matrices in finite Markov processes

The problem of determining the transient and differential matrices in finite Markov processes is considered. New polynomial time algorithms for determining the considered matrices in Markov chains are proposed and grounded. The proposed algorithms find the limit and differential matrices efficiently when the characteristic values of the matrix of probability transition are known; the running time of the algorithms is $O(n^4)$, where $n$ is the number of the states of dynamical system in the Markov process.