Affordable Access

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
Type
Preprint
Publication Date
May 27, 2010
Submission Date
Oct 02, 2009
Identifiers
arXiv ID: 0910.0324
Source
arXiv
License
Yellow
External links

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.

Report this publication

Statistics

Seen <100 times