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Markov Chains

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Poirot

Banned
Feb 15, 2012
250
What is the transition matrix and state space corresponding to a simple random random walk with absorbing barriers at 1 and 5? I know an absorbing barrier will correspong to a row of zeroes but I don't know what a simple random walk is.Thanks
 

CaptainBlack

Well-known member
Jan 26, 2012
890
What is the transition matrix and state space corresponding to a simple random random walk with absorbing barriers at 1 and 5? I know an absorbing barrier will correspong to a row of zeroes but I don't know what a simple random walk is.Thanks
Equal probability of +1, -1.

CB
 
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Poirot

Banned
Feb 15, 2012
250
Sorry I don't understand what you mean. Can you give me the matrix?
 

CaptainBlack

Well-known member
Jan 26, 2012
890
Sorry I don't understand what you mean. Can you give me the matrix?
Something like:

\[A=\left[ \begin{array}{ccccc}1& 0 & 0 & 0 & 0 \\ 0.5 & 0 & 0.5 & 0 & 0 \\ 0 & 0.5 & 0 & 0.5 & 0
\\ 0 & 0 & 0.5 & 0 & 0.5 \\ 0 & 0 & 0 & 0 & 1 \end{array} \right] \]

CB