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Grouping of states of a Markov chain: Consider that three states of the Markov chain {Xn} above are grouped together as follows: Yn is said to be in state 0 if both the (n − 1) th and nth tosses result in Heads and 1 otherwise, (i.e. state 0 for HH and state 1 for HT, TH, TT). Show that the chain {Yn} is non-Markovian. If the states of a Markov chain are grouped or lumped together, the new chain does not, in general, have the Markov property

Grouping of states of a Markov chain: Consider that three states of the Markov chain {Xn} above are grouped together as follows: Yn is said to be in state 0 if both the (n − 1) th and nth tosses result in Heads and 1 otherwise, (i.e. state 0 for HH and state 1 for HT, TH, TT). Show that the chain {Yn} is non-Markovian. If the states of a Markov chain are grouped or lumped together, the new chain does not, in general, have the Markov property

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 18EQ
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 Grouping of states of a Markov chain: Consider that three states of the Markov chain {Xn}
above are grouped together as follows: Yn is said to be in state 0 if
both the (n − 1) th and nth tosses result in Heads and 1 otherwise, (i.e. state 0 for HH and state
1 for HT, TH, TT). Show that the chain {Yn} is non-Markovian.
If the states of a Markov chain are grouped or lumped together, the new chain does not, in
general, have the Markov property.

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