  In this paper we prove exact forms of large deviations for local times and
intersection local times of fractional Brownian motions and Riemann-Liouville
processes. We also show that a fractional Brownian motion and the related
Riemann-Liouville process behave like constant multiples of each other with
regard to large deviations for their local and intersection local times. As a
consequence of our large deviation estimates, we derive laws of iterated
logarithm for the corresponding local times. The key points of our methods: (1)
logarithmic superadditivity of a normalized sequence of moments of
exponentially randomized local time of a fractional Brownian motion; (2)
logarithmic subadditivity of a normalized sequence of moments of exponentially
randomized intersection local time of Riemann-Liouville processes; (3)
comparison of local and intersection local times based on embedding of a part
of a fractional Brownian motion into the reproducing kernel Hilbert space of
the Riemann-Liouville process.
