Local linear estimator for stochastic differential equations driven by \(\alpha\)-stable Lévy motions

DOI10.1007/s11425-013-4628-7zbMath1396.62064OpenAlexW1561054709MaRDI QIDQ476746

Jiangsheng Yi, Zheng Yan Lin, Yu Ping Song

Publication date: 2 December 2014

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-013-4628-7

zbMATH Keywords

consistencybias reductioncentral limit theoremlocal linear estimatordrift coefficientstable Lévy motion

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Markov processes: estimation; hidden Markov models (62M05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (4)

Convoluted smoothed kernel estimation for drift coefficients in jump-diffusion models ⋮ Estimation of state-dependent jump activity and drift for Markovian semimartingales ⋮ Nonparametric Gaussian inference for stable processes ⋮ Nonparametric estimation of periodic signal disturbed by α-stable noises

Uses Software

• KernSmooth

Cites Work

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• A simple approach to the parametric estimation of potentially nonstationary diffusions
• Discretization of processes.
• Estimating the degree of activity of jumps in high frequency data
• Estimation of parameters for diffusion processes with jumps from discrete observations
• Ergodicity and exponential \(\beta\)-mixing bounds for multidimensional diffusions with jumps
• Basic properties of strong mixing conditions. A survey and some open questions
• Testing for jumps in a discretely observed process
• Empirical likelihood estimation of discretely sampled processes of OU type
• Variable bandwidth and local linear regression smoothers
• On the functional estimation of jump-diffusion models.
• On multidimensional Ornstein-Uhlenbeck processes driven by a general Lévy process
• Multivariate locally weighted least squares regression
• Optimal global rates of convergence for nonparametric regression
• Nonparametric statistics for stochastic processes
• Nadaraya-Watson estimator for stochastic processes driven by stable Lévy motions
• Approximate self-weighted LAD estimation of discretely observed ergodic Ornstein-Uhlenbeck processes
• Least squares estimator for Ornstein-Uhlenbeck processes driven by \(\alpha \)-stable motions
• Microstructure noise in the continuous case: the pre-averaging approach
• The approximate Euler method for Lévy driven stochastic differential equations
• Empirical likelihood-based inference for nonparametric recurrent diffusions
• Nonparametric inference of discretely sampled stable Lévy processes
• Fractional Fokker–Planck equation for nonlinear stochastic differential equations driven by non-Gaussian Lévy stable noises
• NONPARAMETRIC ESTIMATION OF SECOND-ORDER STOCHASTIC DIFFERENTIAL EQUATIONS
• Local Linear Estimation of Second-Order Diffusion Models
• REWEIGHTED FUNCTIONAL ESTIMATION OF DIFFUSION MODELS
• Estimation of the drift for diffusion process
• Robust Locally Weighted Regression and Smoothing Scatterplots
• Design-adaptive Nonparametric Regression
• Intentionally Biased Bootstrap Methods
• A Reexamination of Diffusion Estimators With Applications to Financial Model Validation
• Transform Analysis and Asset Pricing for Affine Jump-diffusions
• The Relationship between Variable Selection and Data Agumentation and a Method for Prediction
• Local Linear Estimation of Recurrent Jump—Diffusion Models
• Fully Nonparametric Estimation of Scalar Diffusion Models
• A Tale of Two Time Scales

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