Parameter estimation for stochastic equations with additive fractional Brownian sheet

DOI10.1007/s11203-007-9019-7zbMath1204.60031OpenAlexW2117016916MaRDI QIDQ623488

Tommi Sottinen, Ciprian A. Tudor

Publication date: 5 February 2011

Published in: Statistical Inference for Stochastic Processes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11203-007-9019-7

zbMATH Keywords

Malliavin calculusmaximum likelihood estimatorfractional Brownian sheetgirsanov transform

Mathematics Subject Classification ID

Random fields; image analysis (62M40) Gaussian processes (60G15) Signal detection and filtering (aspects of stochastic processes) (60G35) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (9)

An identification problem for systems with additive fractional Brownian field ⋮ Drift parameter estimation in fractional diffusions driven by perturbed random walks ⋮ An exponential nonuniform Berry-Esseen bound for the fractional Ornstein-Uhlenbeck process ⋮ Least squares estimator for the parameter of the fractional Ornstein-Uhlenbeck sheet ⋮ Wiener integrals with respect to the Hermite random field and applications to the wave equation ⋮ Maximum likelihood estimator for the sub-fractional Brownian motion approximated by a random walk ⋮ Some linear fractional stochastic equations ⋮ Minimum distance parameter estimation for a stochastic equation with additive fractional Brownian sheet ⋮ Maximum-likelihood estimators and random walks in long memory models

Cites Work

• On the Wiener integral with respect to the fractional Brownian motion
• On the equivalence of multiparameter Gaussian processes
• An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions
• Fractional Brownian sheet
• Itô formula and local time for the fractional {B}rownian sheet
• Statistical inference with fractional Brownian motion
• Statistical analysis of the fractional Ornstein--Uhlenbeck type process
• Regularization of differential equations by fractional noise.
• Hyperbolic Stochastic Partial Differential Equations with Additive Fractional Brownian Sheet
• Some linear fractional stochastic equations
• Parameter estimation and optimal filtering for fractional type stochastic systems
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