Transfer Matrix Interpretation

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jk22
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Transfer Matrix Interpretation

Postby jk22 » Mon Jul 05, 2010 11:57 am

Hi, nice to meet you.

I'm trying to understand the formalism of transition matrices in probability :

a) if I have a state determined by (s1,...sr), where si is in {h,t} (head tail), the probability of head were p, and tail : q=1-p.

what Does the matrix :

mean :

s1 becomes head (p), and s2-sr becomes tail (q) ?

b) how to prove that : ?

thx.

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Martingale
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Re: Transfer Matrix Interpretation

Postby Martingale » Mon Jul 05, 2010 5:13 pm

jk22 wrote:Hi, nice to meet you.

I'm trying to understand the formalism of transition matrices in probability :

a) if I have a state determined by (s1,...sr), where si is in {h,t} (head tail), the probability of head were p, and tail : q=1-p.

what Does the matrix :

mean :

s1 becomes head (p), and s2-sr becomes tail (q) ?

b) how to prove that : ?

thx.


is the last row in M supposed to just be [p,0,0...,0]?

is M supposed to be a Markov transition matrix?

is , times the vector ?

jk22
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Re: Transfer Matrix Interpretation

Postby jk22 » Mon Jul 05, 2010 8:44 pm

Hello,

yes, I read it like that. M is said to be a stochastic matrix.

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Re: Transfer Matrix Interpretation

Postby Martingale » Mon Jul 05, 2010 8:56 pm

jk22 wrote:Hello,

yes, I read it like that. M is said to be a stochastic matrix.



then how can the bottom row be [p,0,...0]

shouldn't each row add to 1?

jk22
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Re: Transfer Matrix Interpretation

Postby jk22 » Sun Jul 11, 2010 9:50 am

Hi,

if it were a sub-stochastic matrix, it wouldn't need this condition ?

thanks.

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Re: Transfer Matrix Interpretation

Postby Martingale » Sun Jul 11, 2010 3:21 pm

jk22 wrote:Hi,

if it were a sub-stochastic matrix, it wouldn't need this condition ?

thanks.


Did you remove an absorbing state?


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