Nnon-negative matrices and markov chains pdf files

The pis a probability measure on a family of events f a eld in an eventspace 1 the set sis the state space of the process, and the. Regular markov chains a transition matrix p is regular if some power of p has only positive entries. Given an initial distribution px i p i, the matrix p allows us to compute the the distribution at any subsequent time. As i will want to examine some real and theoretical markovian matrices and their associated eigenvalues, it is proper to begin by restating the perronfrobenius theorem frobenius, 1912, seneta, 1973 for primi. A generalized markov chain satisfying is called generalized. Definition of nonnegative matrix and primitive matrix. T is primitive if there exists a positive integer k such that tk 0. A markov chain is a regular markov chain if its transition matrix is regular. Nonnegative matrices and markov chains springerlink. Since its inception by perron and frobenius, the theory of nonnegative matrices has developed enormously and is now being used and extended in applied fields of study as diverse as probability theory, numerical analysis, demography, mathematical economics, and dynamic programming, while its. Nonnegative matrices and markov chains part i fundamental concepts and results in the theory of nonnegative matrices 1.