  This paper is concerned with the study of linear cocycles over uniformly
ergodic Markov shifts on a compact space of symbols. We establish the joint
H\"older continuity of the maximal Lyapunov exponent as a function of the
cocycle and the transition kernel in the vicinity of any irreducible cocycle
with simple maximal Lyapunov exponent. Our approach, via Furstenberg's formula,
shows the H\"older continuous dependence on the data of the stationary measure
of the projective cocycle and in particular provides a more computable H\"older
exponent.
