MHB Understanding Markov Chains: Transition Matrix and State Space Explained

[Poirot1]

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]

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

 

[Poirot1]

Sorry I don't understand what you mean. Can you give me the matrix?

 

[CaptainBlack]

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