Definitions of state transitions

Question 1

Class

Answer 1

irreducible class of states

Question 2

what happens when there is only one irreducible class

Answer 2

Markov Chain is irreducible

Question 3

What happens when a state doesn’t intercommunicate with any other state

Answer 3

Forms its own irreducible class

Question 4

State i and state j intercommunicate if ?

Answer 4

i goes to j and j goes to i

Question 5

Recurrent State

Answer 5

Eventual return to state i is certain (Probability of 1 )

Question 6

Transient

Answer 6

Eventual return to state i is uncertain uncertain

Question 7

Mean recurrence time (u )

Answer 7

average number of steps until the chain first returns to state i given that it starts in state i

Question 8

Positive recurrent

Answer 8

if the mean recurrence time is finite ( time to come back to orginal state is finite

Question 9

Null recurrent

Answer 9

mean recurrence time is infinity

Question 10

Period of state i

Answer 10

greatest common divisor of the set of integers n>= 1 s.t pii(n) >. 0

Question 11

Aperiodic

Answer 11

it the greatest common divisor of a set of integers is 1
if probaility of returning to a state is impossible it is also aperiodic