What is a homogeneous markov chain?
I have started learning about markov chains but I am struck with the concept of homogeneous markov chain.
According textbook defination of Probability, Random variables and Stochastic process by Papoulis and Unnikrishna Pillai,
It says that,
A Markov chain is said to be homogeneous in time if $P_ij(m,n)$ depends only the difference n-m.
I am unable to interpret properly, please help me to understand what does the time difference here meant?
My thought:
If at time m, the state is i and then after ( n-m ) time the system will be in j state?
Please correct me if I am wrong.
markov-chains
asked Nov 25 at 7:03
Anil
1064
add a comment |
I have started learning about markov chains but I am struck with the concept of homogeneous markov chain.
According textbook defination of Probability, Random variables and Stochastic process by Papoulis and Unnikrishna Pillai,
It says that,
A Markov chain is said to be homogeneous in time if $P_ij(m,n)$ depends only the difference n-m.
I am unable to interpret properly, please help me to understand what does the time difference here meant?
My thought:
If at time m, the state is i and then after ( n-m ) time the system will be in j state?
Please correct me if I am wrong.
markov-chains
asked Nov 25 at 7:03
Anil
1064
add a comment |
I have started learning about markov chains but I am struck with the concept of homogeneous markov chain.
According textbook defination of Probability, Random variables and Stochastic process by Papoulis and Unnikrishna Pillai,
It says that,
A Markov chain is said to be homogeneous in time if $P_ij(m,n)$ depends only the difference n-m.
I am unable to interpret properly, please help me to understand what does the time difference here meant?
My thought:
If at time m, the state is i and then after ( n-m ) time the system will be in j state?
Please correct me if I am wrong.
markov-chains
asked Nov 25 at 7:03
Anil
1064
I have started learning about markov chains but I am struck with the concept of homogeneous markov chain.
According textbook defination of Probability, Random variables and Stochastic process by Papoulis and Unnikrishna Pillai,
It says that,
A Markov chain is said to be homogeneous in time if $P_ij(m,n)$ depends only the difference n-m.
I am unable to interpret properly, please help me to understand what does the time difference here meant?
My thought:
If at time m, the state is i and then after ( n-m ) time the system will be in j state?
Please correct me if I am wrong.
markov-chains
markov-chains
asked Nov 25 at 7:03
Anil
1064
asked Nov 25 at 7:03
Anil
1064
asked Nov 25 at 7:03
Anil
1064
asked Nov 25 at 7:03
Anil
1064
asked Nov 25 at 7:03
Anil
1064
1064
add a comment |
add a comment |
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