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$X$ is a Markov process with state space $(1,2,3)$. How can I find the matrices of transition probabilities $P(t)$ if the generator is \begin{bmatrix}-2&2&0\\2&-4&2\\0&2&-2\end{bmatrix}?

Can I use Kolmogorov forward equation $P'(t)=P(t)Q$ where $Q$ is the generator for this problem?

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