I have the following system of ODEs $$d\mathbf{x}\left(t\right)=A\left(s\left(t\right)\right)\mathbf{x}\left(t\right)dt$$ where $s\left(t\right)\in\left\{ 1,2\right\}$ is the state of the system which follows a (2-state) Markov switching process. The system contains both predetermined variables and forward-looking variables and can be solved analytically for each realization of $\left\{ s\left(t\right)\right\} _{t=0}^{\infty}$. Can I compute the analytical expression for $\mathbb{E}\left[x\left(0\right)\right]$?


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