A Donsker theorem for Lévy measures

DOI10.1016/j.jfa.2012.08.012zbMath1310.60056arXiv1201.0590OpenAlexW2126716816MaRDI QIDQ1762342

Richard Nickl, Markus Reiss

Publication date: 23 November 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.0590

zbMATH Keywords

pseudo-differential operatorssmoothed empirical processesuniform central limit theoremnonlinear inverse problemjump measure

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Generalized stochastic processes (60G20) Functional limit theorems; invariance principles (60F17)

Related Items (26)

High-frequency Donsker theorems for Lévy measures ⋮ The mathematical work of Evarist Giné ⋮ Multiscale methods for shape constraints in deconvolution: confidence statements for qualitative features ⋮ Nonparametric inference on Lévy measures and copulas ⋮ On a linear functional for infinitely divisible moving average random fields ⋮ Information bounds for inverse problems with application to deconvolution and Lévy models ⋮ Adaptive nonparametric estimation for Lévy processes observed at low frequency ⋮ A uniform central limit theorem and efficiency for deconvolution estimators ⋮ Nonparametric low-frequency Lévy copula estimation in a general framework ⋮ Testing the characteristics of a Lévy process ⋮ On infinitely divisible distributions with polynomially decaying characteristic functions ⋮ Inference on the Lévy measure in case of noisy observations ⋮ Quantile estimation for Lévy measures ⋮ Adaptive pointwise estimation for pure jump Lévy processes ⋮ Spectral-free estimation of Lévy densities in high-frequency regime ⋮ A non-parametric Bayesian approach to decompounding from high frequency data ⋮ Sup-norm convergence rates for Lévy density estimation ⋮ Efficient nonparametric inference for discretely observed compound Poisson processes ⋮ Multiscale scanning in inverse problems ⋮ Weak convergence of the empirical truncated distribution function of the Lévy measure of an Itō semimartingale ⋮ Estimation and Calibration of Lévy Models via Fourier Methods ⋮ Adaptive quantile estimation in deconvolution with unknown error distribution ⋮ Bootstrap confidence bands for spectral estimation of Lévy densities under high-frequency observations ⋮ Nonparametric inference on Lévy measures of compound Poisson-driven Ornstein-Uhlenbeck processes under macroscopic discrete observations ⋮ Bernstein-von Mises theorems for statistical inverse problems. II: Compound Poisson processes ⋮ On detecting changes in the jumps of arbitrary size of a time-continuous stochastic process

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