  We consider the problem of estimating the top Lyapunov exponents for
Markovian products of positive matrices. We define a new transfer operator as a
matrix of classical transfer operators and prove its spectral properties. With
the spectral properties, we generalize (and provide a more theoretically
rigorous foundation for) an algorithm that was introduced informally by Bai and
formally by Pollicott based on dynamical zeta functions.
