Nonparametric adaptive estimation for pure jump Lévy processes

DOI10.1214/09-AIHP323zbMath1201.62042arXiv0806.3371MaRDI QIDQ1958507

Valentine Genon-Catalot, Fabienne Comte

Publication date: 4 October 2010

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.3371

zbMATH Keywords

deconvolutionLévy processadaptive estimationnonparametric projection estimator

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Markov processes: estimation; hidden Markov models (62M05)

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Cites Work

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• Nonparametric estimation for Lévy processes from low-frequency observations
• On the optimal rates of convergence for nonparametric deconvolution problems
• Nonparametric inference for Lévy-driven Ornstein-Uhlenbeck processes
• Pointwise deconvolution with unknown error distribution
• Minimum contrast estimators on sieves: Exponential bounds and rates of convergence
• Concentration around the mean for maxima of empirical processes
• Hyperbolic distributions in finance
• Bilateral gamma distributions and processes in financial mathematics
• Penalized contrast estimator for adaptive density deconvolution
• Risk bounds for the non-parametric estimation of Lévy processes
• On the effect of estimating the error density in nonparametric deconvolution
• Nonparametric estimation of the canonical measure for infinitely divisible distributions
• Financial Modelling with Jump Processes
• Parametric Estimation for Subordinators and Induced OU Processes

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