every stochastic matrix defines a markov chain?
0
Maybe the Question is obvious, but if $P$ is a $( n times n)$ stochastic matrix, can I associate it with a discrete time finite markov chain?
probability markov-chains
asked Dec 7 at 22:45
wayne
492112
add a comment |
0
Maybe the Question is obvious, but if $P$ is a $( n times n)$ stochastic matrix, can I associate it with a discrete time finite markov chain?
probability markov-chains
asked Dec 7 at 22:45
wayne
492112
True by definition, isn't it?
– Aditya Dua
Dec 7 at 22:48
markov chains are often defined as a stochastic process which satisfies the markov property. But if I have a stochastic matrix $P$, can I definitely associtate it with a markov chain?
– wayne
Dec 7 at 23:01
@wayne Markov property tells you how to write down finite dimensional distributions and any consistent family of finite dimensional distributions corresponds to a process. This is Kolmogorov's Consistency Theorem.
– Kavi Rama Murthy
Dec 7 at 23:26
Thanks! I was looking for this theorem
– wayne
Dec 9 at 15:55
add a comment |
0
0
0
Maybe the Question is obvious, but if $P$ is a $( n times n)$ stochastic matrix, can I associate it with a discrete time finite markov chain?
probability markov-chains
asked Dec 7 at 22:45
wayne
492112
Maybe the Question is obvious, but if $P$ is a $( n times n)$ stochastic matrix, can I associate it with a discrete time finite markov chain?
probability markov-chains
probability markov-chains
asked Dec 7 at 22:45
wayne
492112
asked Dec 7 at 22:45
wayne
492112
asked Dec 7 at 22:45
wayne
492112
asked Dec 7 at 22:45
wayne
492112
asked Dec 7 at 22:45
wayne
492112
492112
True by definition, isn't it?
– Aditya Dua
Dec 7 at 22:48
markov chains are often defined as a stochastic process which satisfies the markov property. But if I have a stochastic matrix $P$, can I definitely associtate it with a markov chain?
– wayne
Dec 7 at 23:01
@wayne Markov property tells you how to write down finite dimensional distributions and any consistent family of finite dimensional distributions corresponds to a process. This is Kolmogorov's Consistency Theorem.
– Kavi Rama Murthy
Dec 7 at 23:26
Thanks! I was looking for this theorem
– wayne
Dec 9 at 15:55
add a comment |
True by definition, isn't it?
– Aditya Dua
Dec 7 at 22:48
markov chains are often defined as a stochastic process which satisfies the markov property. But if I have a stochastic matrix $P$, can I definitely associtate it with a markov chain?
– wayne
Dec 7 at 23:01
@wayne Markov property tells you how to write down finite dimensional distributions and any consistent family of finite dimensional distributions corresponds to a process. This is Kolmogorov's Consistency Theorem.
– Kavi Rama Murthy
Dec 7 at 23:26
Thanks! I was looking for this theorem
– wayne
Dec 9 at 15:55
True by definition, isn't it?
– Aditya Dua
Dec 7 at 22:48
True by definition, isn't it?
– Aditya Dua
Dec 7 at 22:48
markov chains are often defined as a stochastic process which satisfies the markov property. But if I have a stochastic matrix $P$, can I definitely associtate it with a markov chain?
– wayne
Dec 7 at 23:01
markov chains are often defined as a stochastic process which satisfies the markov property. But if I have a stochastic matrix $P$, can I definitely associtate it with a markov chain?
– wayne
Dec 7 at 23:01
@wayne Markov property tells you how to write down finite dimensional distributions and any consistent family of finite dimensional distributions corresponds to a process. This is Kolmogorov's Consistency Theorem.
– Kavi Rama Murthy
Dec 7 at 23:26
@wayne Markov property tells you how to write down finite dimensional distributions and any consistent family of finite dimensional distributions corresponds to a process. This is Kolmogorov's Consistency Theorem.
– Kavi Rama Murthy
Dec 7 at 23:26
Thanks! I was looking for this theorem
– wayne
Dec 9 at 15:55
Thanks! I was looking for this theorem
– wayne
Dec 9 at 15:55
add a comment |
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True by definition, isn't it?
– Aditya Dua
Dec 7 at 22:48
markov chains are often defined as a stochastic process which satisfies the markov property. But if I have a stochastic matrix $P$, can I definitely associtate it with a markov chain?
– wayne
Dec 7 at 23:01
@wayne Markov property tells you how to write down finite dimensional distributions and any consistent family of finite dimensional distributions corresponds to a process. This is Kolmogorov's Consistency Theorem.
– Kavi Rama Murthy
Dec 7 at 23:26
Thanks! I was looking for this theorem
– wayne
Dec 9 at 15:55