Please use this identifier to cite or link to this item: http://hdl.handle.net/1783.1/34955

LARGE DEVIATIONS FOR LOCAL TIMES AND INTERSECTION LOCAL TIMES OF FRACTIONAL BROWNIAN MOTIONS AND RIEMANN-LIOUVILLE PROCESSES

Authors Chen, Xia
Li, Wenbo V.
Rosinski, Jan
Shao, Qi-Man View this author's profile
Issue Date 2011
Source Annals of probability , v. 39, (2), March 2011, p. 729-778
Summary 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.
Subjects
ISSN 0091-1798
Language English
Format Article
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