Markov chains are a relatively simple but very interesting and useful class of random processes. A Markov chain describes a system whose state changes over time. The changes are not …

A transition matrix (also known as a stochastic matrix ) or Markov matrix is a matrix in which each column is a probability vector. An example would be the matrix representing how the …

A Markov chain with state space V and transition matrix P can be represented by a labeled directed graph G pV ; Eq, where edges are given by transitions with nonzero probability

Irreducible Markov chains. If the state space is finite and all states communicate (that is, the Markov chain is irreducible) then in the long run, regardless of the initial condition, the Markov …

WHAT IS A HIDDEN MARKOV MODEL (HMM)? A Hidden Markov Model, is a stochastic model where the states of the model are hidden. Each state can emit an output which is observed. …

We will see how the Markov property allows us to reduce many problems concerning a Markov chain to matrix equations, which can then be solved with the techniques of linear algebra.

Sequence is called a Markov chain if we have a collection of numbers Pij (one for each pair xed i; j 2 f0; 1; : : : ; Mg) such that whenever the system is in state i, there is probability Pij that …