# Do transient states have periods?

## Do transient states have periods?

In a class, all the states have the same period. In some article, by definition A has a period=0. It’s a transient state. B and C have a period of one ( there is loop on themselves).

How do you calculate state period?

The period of a state i is the largest integer d satisfying the following property: p(n)ii=0, whenever n is not divisible by d. The period of i is shown by d(i). If p(n)ii=0, for all n>0, then we let d(i)=∞.

What is a class in Markov chain?

A communication class C ⊆ S is a set of states whose members communicate, i.e. i ↔ j for all i, j ∈ C, , and no state in C communicates with any state not in C. A finite Markov chain (or equivalently, its transition matrix T) is irreducible, if it has a single communicating class C = S.

### What is a state in Markov chain?

Definition: The state of a Markov chain at time t is the value of Xt. For example, if Xt = 6, we say the process is in state 6 at time t. Definition: The state space of a Markov chain, S, is the set of values that each Xt can take. For example, S = {1,2,3,4,5,6,7}.

How do you find the period of state in a Markov chain?

The period of a state i is d(i)=gcd{n:Pnii>0}. If two states i and j communicate, that is, there exist m,n>0 such that Pnij>0 and Pmji>0, then d(i)=d(j). By inspection, states 1,2,3,5,6 all communicate.

How do you calculate the period of a Markov chain?

Pr(Xn′=i|X0=i)>0. Otherwise (k > 1), the state is said to be periodic with period k. A Markov chain is aperiodic if every state is aperiodic. The term periodicity describes whether something (an event, or here: the visit of a particular state) is happening at a regular time interval.

#### How do you identify a Markov Chain class?

To create a subchain: Identify the recurrent class in the Markov chain. Identify the bin number of the recurrent class….Identify Classes in Markov Chain

1. Class indices, bins.
2. Class memberships, ClassStates.
3. Whether the classes are recurrent, ClassRecurrence.
4. Class periods, ClassPeriod.

What is transient and recurrent states?

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.

How do you classify states in a Markov chain?

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. Proof.

## How do you know if a state is recurrent or transient?

Is the Markov chain irreducible and aperiodic?

As the given Markov Chain is irreducible, the rest of the states of the Markov Chain are also aperiodic. Note that, all the elements of P(2) are positive.

Is periodicity a class property?

Periodicity is a class property.