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

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.

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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

Information

Published: March 2011
First available in Project Euclid: 25 February 2011

zbMATH: 1229.60044
MathSciNet: MR2789511
Digital Object Identifier: 10.1214/10-AOP566

Subjects:
Primary: 60F10 , 60G15 , 60G18 , 60G22 , 60J55

Keywords: fractional Brownian motion , Intersection local time , large deviations , Law of iterated logarithm , Local time , Riemann–Liouville process

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 2 • March 2011
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