# What is absorbing Markov chain with example?

What is absorbing Markov chain with example?

## What is absorbing Markov chain with example?

A simple example of an absorbing Markov chain is the drunkard’s walk of length n + 2 n + 2 n+2. In the drunkard’s walk, the drunkard is at one of n n n intersections between their house and the pub. The drunkard wants to go home, but if they ever reach the pub (or the house), they will stay there forever.

How do I know if my Markov chain is absorbing?

Absorbing Markov Chains

1. A Markov chain is an absorbing Markov chain if it has at least one absorbing state.
2. If a transition matrix T for an absorbing Markov chain is raised to higher powers, it reaches an absorbing state called the solution matrix and stays there.

What is the difference between a transient state and an absorbing state?

Absorbing Markov Chains A Markov chain is said to be an absorbing Markov chain if: It has at least one absorbing state. From every state in the Markov chain there exists a sequence of state transitions with nonzero probability that lead to an absorbing state. These nonabsorbing states are called transient states.

### Can a Markov chain be both regular and absorbing?

The general observation is that a Markov chain can be neither regular nor absorbing.

Is an absorbing state recurrent?

You are correct: an absorbing state must be recurrent. To be precise with definitions: given a state space X and a Markov chain with transition matrix P defined on X. A state x∈X is absorbing if Pxx=1; neccessarily this implies that Pxy=0,y≠x.

Is an absorbing state transient?

absorbing is called transient. Hence, in an absorbing Markov chains, There are absorbing states or transient states. Example: This is a ITMC with two absorbing states A and E.

#### Can an absorbing state be transient?

Can a state be both recurrent and absorbing?

Are all absorbing states recurrent?