Absorbing states

State i is said to be an absorbing state if it is impossible for a system to leave that state once it reaches it. For a state to be an absorbing state, the probability of staying in the same state should be 1, and all the other probabilities should be 0:

In a Markov chain, if all the states are absorbing, then we call it an absorbing Markov chain:

Again, we can add a very simple method to check for absorbing states in our MarkovChain class:

def is_absorbing(self, state):
 """
 Checks if the given state is absorbing.

 Parameters
 ----------
 state: str
 The state for which we need to check whether it's absorbing
 or not.
 """
 state_index = self.index_dict[state]
 if self.transition_matrix[state_index, state_index]

We can again check whether our state in the example is absorbing by creating a Markov chain and using the is_absorbing method:

>>> absorbing_matrix = [[0, 1, 0],
                        [0.5, 0, 0.5],
                        [0, 0, 1]]
>>> absorbing_chain = MarkovChain(transition_matrix=absorbing_matrix,
                                  states=['A', 'B', 'C'])
>>> absorbing_chain.is_absorbing('A')
False
>>> absorbing_chain.is_absorbing('C')
True