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Which states are recurrent and which states are transient?
A recurrent state has the property that a Markov chain starting at this state returns to this state infinitely often, with probability 1. A transient state has the property that a Markov chain starting at this state returns to this state only finitely often, with probability 1.
Are all irreducible transition matrix recurrent?
Therefore, in any class, either all states are recurrent or all are transient. In particular, if the chain is irreducible, then either all states are recurrent or all are transient. In light of this proposition, we can classify each class, and an irreducible Markov chain, as recurrent or transient.
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 there a guarantee that a process will never return to a transient state?
There is some possibility (a nonzero probability) that a process beginning in a transient state will never return to that state. There is a guarantee that a process beginning in a recurrent state will return to that state.
How are positive recurrent states different from positive Markov chains?
An aperiodic Markov chain with positive recurrent states While a recurrent state has the property that the Markov chain is expected to return to the state an infinite number of times, the Markov chain is not necessarily expected to return even once within a finite number of steps.
When is a state known as a transient state?
If there is a possibility of leaving the state and never returning, then the state is not very connected at all, so it is known as transient. In addition to the traditional definition regarding probability of return, there are other equivalent definitions of transient states. { X 0, X 1, …
What does transience and recurrence mean in a stochastic process?
Log in here. A stochastic process contains states that may be either transient or recurrent; transience and recurrence describe the likelihood of a process beginning in some state of returning to that particular state. There is some possibility (a nonzero probability) that a process beginning in a transient state will never return to that state.