Parameter estimations for the sub-fractional Brownian motion with drift at discrete observation

DOI10.1214/14-BJPS246zbMath1416.62472MaRDI QIDQ890275

Nenghui Kuang, Bing-quan Liu

Publication date: 10 November 2015

Published in: Brazilian Journal of Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.bjps/1442513446

zbMATH Keywords

Malliavin calculusStein's methodmaximum likelihood estimatorsub-fractional Brownian motion

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Fractional processes, including fractional Brownian motion (60G22) Non-Markovian processes: estimation (62M09) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (11)

Asymptotic behaviours for maximum likelihood estimator of drift parameter in α-Wiener bridge process ⋮ Least squares estimation for the drift parameters in the sub-fractional Vasicek processes ⋮ Parametric estimation for linear stochastic differential equations driven by sub-fractional Brownian motion ⋮ Least squares type estimators for the drift parameters in the sub-bifractional Vasicek processes ⋮ Fractional processes and their statistical inference: an overview ⋮ Optimal estimation of a signal perturbed by a sub-fractional Brownian motion ⋮ Instrumental variable estimation for stochastic differential equations linear in drift parameter and driven by a sub-fractional Brownian motion ⋮ Nonparametric estimation of linear multiplier for processes driven by subfractional Brownian motion ⋮ Maximum likelihood estimation for sub-fractional Vasicek model ⋮ Nonparametric estimation of trend for stochastic differential equations driven by sub-fractional Brownian motion ⋮ Berry-Esséen bounds and almost sure CLT for the quadratic variation of the sub-bifractional Brownian motion

Uses Software

• longmemo

Cites Work

• Exact maximum likelihood estimators for drift fractional Brownian motion at discrete observa\-tion
• Stein estimation for the drift of Gaussian processes using the Malliavin calculus
• Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields
• Parameter estimation for fractional Ornstein-Uhlenbeck processes
• Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series
• Sub-fractional Brownian motion and its relation to occupation times
• Parametric estimation for sub-fractional Ornstein-Uhlenbeck process
• Maximum likelihood estimator for the sub-fractional Brownian motion approximated by a random walk
• Central limit theorems for multiple stochastic integrals and Malliavin calculus
• The Malliavin Calculus and Related Topics
• Long‐Memory Time Series
• Estimators for the Drift of Subfractional Brownian Motion
• The asymptotic theory of linear time-series models
• Stochastic calculus with respect to Gaussian processes
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