Hölder continuity of the Lyapunov exponents of linear cocycles over hyperbolic maps

Given a hyperbolic homeomorphism on compact metric space, consider the space of linear cocycles over this base dynamics which are Hölder continuous and whose projective actions partially dynamical systems. We prove that locally near any typical cocycle, Lyapunov exponents functions relative to uniform topology. This result is obtained as consequence large deviations type estimate in cocycles. As byproduct our approach, we also establish other statistical properties for iterates such cocycles, namely central limit theorem principle.