# Questions tagged [transition-matrix]

A matrix associated to a transition of a Markov chain. The entries of this matrix represents a probability with the sum of a whole column being $1$.

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### Continuous time Markov Processes, transition rate matrix Q

I have these lecture notes on continuous time Markov Processes: CTMPs I don't seem to understand the relation $Q=P'(0)$, for P: the transition probability matric and Q: the transition rate matrix. ...
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### Calculate $P_{BB}^{n}$ using the periodicity of a Markov chain

I want to compute the probability of $P_{BB}^{n}$ with the following transition matrix: \begin{pmatrix} 0 & 1/2 & 0 & 1/2 & 0 \\ 0 & 0 & 2/3 & 0 & 1/3 \...
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### If all the elements in the main diagonal of a transition matrix are non-zero, is it possible that the Markov chain is not reversible?

I understand that a Markov chain is reversible if $\pi_{i}P_{ij} = \pi_{j}P_{ji}$ and I was looking for some examples of non-reversible Markov chains. I noticed that in all the examples I saw, at ...
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