MHB Understanding Markov Chains: Transition Matrix and State Space Explained

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The discussion focuses on the transition matrix and state space for a simple random walk with absorbing barriers at states 1 and 5. A simple random walk involves equal probabilities of moving to adjacent states, either +1 or -1. The transition matrix provided illustrates how the probabilities are structured, with absorbing barriers represented by rows of zeroes. Specifically, states 1 and 5 are absorbing, meaning once reached, the process cannot leave these states. Understanding this matrix is crucial for analyzing the behavior of the random walk.
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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
 
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Poirot said:
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
 
Sorry I don't understand what you mean. Can you give me the matrix?
 
Poirot said:
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
 

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