# Are absorbing states recurrent?

**Asked by: Ms. Mozell Shields**

Score: 4.6/5 (60 votes)

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.

Simply so, Are absorbing states transient?

absorbing is called

**transient**. Hence, in an absorbing Markov chains, There are absorbing states or transient states.

In respect to this, What is recurrent state?. In general, a state is said to be recurrent

**if, any time that we leave that state, we will return to that state in the future with probability one**. On the other hand, if the probability of returning is less than one, the state is called transient.

Subsequently, question is, How do you prove a state is recurrent?

We say that a state i is recurrent

**if Pi(Xn = i for infinitely many n) = 1**. Pi(Xn = i for infinitely many n) = 0. Thus a recurrent state is one to which you keep coming back and a transient state is one which you eventually leave for ever.

What are absorbing states?

An absorbing state is

**a state that, once entered, cannot be left**. Like general Markov chains, there can be continuous-time absorbing Markov chains with an infinite state space.

**22 related questions found**

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

However, in that example, the chain itself was not absorbing because it was not possible to transition (even indirectly) from any of the non-absorbing (mover) states to some absorbing (stayer) state. The general observation is that **a Markov chain can be neither regular nor absorbing.**

### How do I know if my Markov chain is absorbing?

**if it has at least one absorbing state**. A state i is an absorbing state if once the system reaches state i, it stays in that state; that is, pii=1.

...

**Absorbing Markov Chains**

- Express the transition matrix in the canonical form as below. ...
- The fundamental matrix F=(I−B)−1.

### What is null recurrent Markov chain?

If **all states in an irreducible Markov chain are** null recurrent, then we say that the Markov chain is null recurrent. If all states in an irreducible Markov chain are transient, then we say that the Markov chain is transient.

### Are recurrent States periodic?

If a state is periodic, **it is positive recurrent**.

### How do you show Markov chain is recurrent?

Transient and Recurrent States: In any Markov chain, define fi = P(Eventually return to state i|X0 = i) = P(Xn = i for some n ≥ 1|X0 = i). **If fi = 1**, then we say that state i is recurrent. Otherwise, if fi < 1, then we say that state i is transient.

### What is steady state and transient state?

Also, a steady state establishes after a specific time in your system. However, a transient state is **essentially the time between the beginning of the event and the steady state**. ... Also, transient time is the time it takes for a circuit to change from one steady state to the next.

### What is persistent state in Markov chain?

Definition 8.2 A state j ∈ S is called persistent **if a process stating in this state**. **has probability one to eventually return to it**, i.e., if fj,j = 1. Otherwise, it is called transient. Suppose that the process started in state i. The probability that it visited state j for.

### What is an example of an absorbing state associated with a transition?

Transitions between states occur instantaneously at each of these finite time intervals. In this simple example, **the state DEAD** can be defined as an absorbing state, since once reached it is not possible to make a transition to any other state.

### When absorbing states are present each row of the transition matrix corresponding to an absorbing state will have?

When absorbing states are present, each row of the transition matrix corresponding to an absorbing state will have a **single 1** and all other probabilities will be 0.

### How can you tell if a Markov chain is regular?

A transition matrix P is regular if some power of P has only positive entries. A Markov chain is a regular Markov chain **if its transition matrix is regular**. For example, if you take successive powers of the matrix D, the entries of D will always be positive (or so it appears). So D would be regular.

### Is stationary distribution unique?

Assuming irreducibility, the **stationary distribution is always unique if it exists**, and its existence can be implied by positive recurrence of all states. ... The stationary distribution has the interpretation of the limiting distribution when the chain is ergodic.

### What is the period of a transient state?

A system is said to be transient or in a transient state **when a process variable or variables have been changed and the system has not yet reached a steady state**. The time taken for the circuit to change from one steady state to another steady state is called the transient time.

### What is a periodic state?

The states in a recurrent class are periodic if **they can be lumped together**, or grouped, into several subgroups so that all transitions from one group lead to the next group.

### What does null recurrent mean?

If it's null recurrent, that means **π does not exist**, but you still have a guarantee of returning to every state. In other words, even if the concept of a mixing time does not make sense, you still have finite hitting times.

### Can an infinite Markov chain be positive recurrent?

Theorem 1. Given an infinite M.c. Xn,n ≥ 1 suppose all the states com- municate. Then there exists a stationary distribution ˇ iff there exists at least one **positive** recurrent state i. In this case in fact all the states are positive recurrent and the stationary distribution ˇ is unique.

### What is stationary distribution of Markov chain?

The stationary distribution of a Markov chain describes **the distribution of Xt after a sufficiently long time that the distribution of Xt does not change any longer**. To put this notion in equation form, let π be a column vector of probabilities on the states that a Markov chain can visit.

### What is a transition probability?

**the probability of moving from one state of a system into another state**. If a Markov chain is in state i, the transition probability, p_{ij}, is the probability of going into state j at the next time step. i.

### What is a limiting matrix?

The values of the limiting matrix **represent percentages of ending states(columns) given a starting state(index)**. For example, if the starting state was at 1, the end state probabilities would be: 2: 0% 3: 42.86% 4: 28.57%

### Which of the following is not a assumption of Markov chain analysis?

The following is not an assumption of Markov analysis.**There is an infinite number of possible states**. The probability of changing states remains the same over time. We can predict any future state from the previous state and the matrix of transition probabilities.