Mathematics – Probability
Scientific paper
2009-10-02
Mathematics
Probability
To appear in the Annals of Probability
Scientific paper
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.
Chen Xia
Li Wenbo V.
Rosinski Jan
Shao Qi-Man
No associations
LandOfFree
Large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-26010