The Annals of Probability
- Ann. Probab.
- Volume 39, Number 2 (2011), 729-778.
Large deviations for local times and intersection local times of fractional Brownian motions and Riemann–Liouville processes
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.
Ann. Probab., Volume 39, Number 2 (2011), 729-778.
First available in Project Euclid: 25 February 2011
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G22: Fractional processes, including fractional Brownian motion 60J55: Local time and additive functionals 60F10: Large deviations 60G15: Gaussian processes 60G18: Self-similar processes
Chen, Xia; Li, Wenbo V.; Rosiński, Jan; Shao, Qi-Man. Large deviations for local times and intersection local times of fractional Brownian motions and Riemann–Liouville processes. Ann. Probab. 39 (2011), no. 2, 729--778. doi:10.1214/10-AOP566. https://projecteuclid.org/euclid.aop/1298669178