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Sharp Large Deviations for the Fractional Ornstein–Uhlenbeck Process

Bernard Bercu · Laure Coutin · Nicolas Savy

52 citations0/0 files storedTheory of Probability and Its Applications

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Stochastic processes and financial applications Stochastic processes and statistical mechanics Fractional Differential Equations Solutions

Abstract

We investigate the sharp large deviation properties of the energy and the maximum likelihood estimator for the Ornstein–Uhlenbeck process driven by a fractional Brownian motion with Hurst index greater than one half.

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References

1999An Elementary Approach to a Girsanov Formula and Other Analytical Results on Fractional Brownian Motions 2010Parameter estimation for fractional Ornstein–Uhlenbeck processes 2002Statistical Analysis of the Fractional Ornstein–Uhlenbeck Type Process 2006Transformation formulas for fractional Brownian motion 2009Asymptotic properties of MLE for partially observed fractional diffusion system

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2013Distributions of the maximum likelihood and minimum contrast estimators associated with the fractional Ornstein–Uhlenbeck process 2014Parameter estimation based on discrete observations of fractional Ornstein–Uhlenbeck process of the second kind 2023Moderate Deviations for Parameter Estimation in the Fractional Ornstein-Uhlenbeck Processes with Periodic Mean 2014Maximum likelihood estimation for the non-ergodic fractional Ornstein–Uhlenbeck process 2011Minimum contrast estimation in fractional Ornstein-Uhlenbeck process: Continuous and discrete sampling 2016Estimating drift parameters in a fractional Ornstein Uhlenbeck process with periodic mean

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