Parameter estimation for fractional Ornstein-Uhlenbeck processes at discrete observation

DOI10.1016/j.apm.2011.02.047zbMath1225.62116OpenAlexW2095020966MaRDI QIDQ646181

Weidong Xu, Wei-Lin Xiao, Wei-Guo Zhang

Publication date: 11 November 2011

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2011.02.047

zbMATH Keywords

ergodic theoremquadratic variationdiscrete time samplingfractional Ornstein Uhlenbeck processes

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Markov processes: estimation; hidden Markov models (62M05) Diffusion processes (60J60)

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Uses Software

• longmemo

Cites Work

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• Optimum step-stress partially accelerated life tests for the truncated logistic distribution with censoring
• The asymptotic behavior of the R/S statistic for fractional Brownian motion
• Asymptotic properties of MLE for partially observed fractional diffusion system
• Parameter estimation for fractional Ornstein-Uhlenbeck processes
• Estimation of Hurst exponent revisited
• Asymptotic properties of MLE for partially observed fractional diffusion system with dependent noises
• Maximum likelihood estimation for a road traffic network model
• Stochastic analysis of the fractional Brownian motion
• An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions
• Statistical inference for ergodic diffusion processes.
• Fractional {O}rnstein-{U}hlenbeck processes
• Statistical analysis of the fractional Ornstein--Uhlenbeck type process
• Martingale estimation functions for discretely observed diffusion processes
• A fractional linear system view of the fractional Brownian motion
• Sharp Large Deviations for the Fractional Ornstein–Uhlenbeck Process
• TESTS FOR FRACTIONAL INTEGRATION:A MONTE CARLO INVESTIGATION
• The Malliavin Calculus and Related Topics
• Long-Term Memory in Stock Market Prices
• Likelihood Inference for Discretely Observed Nonlinear Diffusions
• ASYMPTOTIC PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATOR FOR STOCHASTIC PARABOLIC EQUATIONS WITH ADDITIVE FRACTIONAL BROWNIAN MOTION
• Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach
• Parameter estimation and optimal filtering for fractional type stochastic systems

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