Abstract
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.
Citation
Xia Chen. Wenbo V. Li. Jan Rosiński. Qi-Man Shao. "Large deviations for local times and intersection local times of fractional Brownian motions and Riemann–Liouville processes." Ann. Probab. 39 (2) 729 - 778, March 2011. https://doi.org/10.1214/10-AOP566
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