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Given a simple CTMC with three states 0,1,2. There are three transitions $0 \rightarrow 1$ (with rate $2u$), $1 \rightarrow 2$ (with rate $u$), $1 \rightarrow 0$ (rate $v$).So $2$ is an absorbing state. Can someone please help me understand how to find the expected time to reach state-2 from state-0? Using the understanding I get, I want to do the analysis on some complex markov chains.

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    Did you try the standard method? That is, introduce the expected time t(x) to reach state 2 starting from state x, find a linear system which the t(x) solve, deduce every t(x), and in particular t(0), which is the expected time you are after.2012-09-02

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