Linear ODEs system with Markov-switching coefficients

by LupinIII   Last Updated February 11, 2019 10:20 AM

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 $\mathbb{E}\left[x\left(0\right)\right]$?



Related Questions



Solving Kolmogorov Equations

Updated August 19, 2017 08:20 AM

If $P$ is irreducible, then $I - P +A$ is invertible

Updated September 25, 2017 13:20 PM