Irreducible Markov Chain

An Irreducible Markov Chain is a Markov Chain where every state can be reached from every other state in a finite number of steps.

This implies that k exists such that p_ij^(k) for all possible values of i and j. In other words, given any initial state and final state which are valid states of the Markov Chain, there will always be a sequence of states such that one can reach the final state from the initial state.

If a Markov Chain is not irreducible , then - (a) It may have one or more absorbing states which will be states from which the process cannot move to any of the other states or (b) It may have a subset of states A from where one cannot move to states outside A

Irreducible Markov Chain

This is a Markov Chain where every state can be reached from every other state in a finite number
of steps.

This implies that k exists such that p _ij^(k) for∀i, j.

If a Markov Chain is not irreducible , then - (a) it may have one or more absorbing states which will be states from which the process cannot move to any of the other states, or (b) it may have a subset of states A from where one cannot move to states outside A , i.e. in A C