2009/10/02 by Xia Chen, Chen, Xia, Wenbo V. Li +5
Economics, Econometrics and Finance · Mathematics · #60F10 #60G15 #60G18 #60G22 #60J55 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.0910.0324
openalex publication_date 2009/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.