Markov Chains

Question 1

Define irreducible

Answer 1

Each state is reachable from any other state given enough time

Question 2

Define periodicity

Answer 2

A state i is said to be period with period d>1 if a return to that state is possible only in a number of steps that is a multiple of d

Question 3

Define aperiodic

Answer 3

A state is said to be aperiodic if it has a period d = 1

Question 4

if all the states are aperiodic then..

Answer 4

The Markov chain is aperiodic

Question 5

all the states have the same period or are all aperiodic then

Answer 5

The Markov chain is irreducible

Question 6

if all the states in an irreducible Markov chain have period d>1

Answer 6

we may describe the chain as periodic with period d