High-frequency Donsker theorems for Lévy measures

DOI10.1007/s00440-014-0607-3zbMath1333.60063arXiv1310.2523OpenAlexW3101841954MaRDI QIDQ2634896

Jakob Söhl, Mathias Trabs, Richard Nickl, Markus Reiss

Publication date: 10 February 2016

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.2523

zbMATH Keywords

Brownian motionGaussian processempirical processLévy processhigh-frequency inferenceDonsker-type functional limit theorems

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Gaussian processes (60G15) Nonparametric estimation (62G05) Central limit and other weak theorems (60F05) Brownian motion (60J65) Functional limit theorems; invariance principles (60F17)

Related Items (13)

Nonparametric inference of gradual changes in the jump behaviour of time-continuous processes ⋮ Low-rank diffusion matrix estimation for high-dimensional time-changed Lévy processes ⋮ Dispersal density estimation across scales ⋮ Minimax rates for the covariance estimation of multi-dimensional Lévy processes with high-frequency data ⋮ Nonparametric implied Lévy densities ⋮ Spectral-free estimation of Lévy densities in high-frequency regime ⋮ A non-parametric Bayesian approach to decompounding from high frequency data ⋮ Efficient nonparametric inference for discretely observed compound Poisson processes ⋮ Weak convergence of the empirical truncated distribution function of the Lévy measure of an Itō semimartingale ⋮ Statistical inference for misspecified ergodic Lévy driven stochastic differential equation models ⋮ 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

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