Penalized nonparametric drift estimation for a continuously observed one-dimensional diffusion process

DOI10.1051/ps/2009016zbMath1395.62257OpenAlexW2005461935MaRDI QIDQ4918488

Dasha Loukianova, Oleg Loukianov, Eva Löcherbach

Publication date: 25 April 2013

Published in: ESAIM: Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/ps/2009016

zbMATH Keywords

model selectiondiffusion processadaptive estimationdeviation inequalitiesmean square estimatorregeneration method

Mathematics Subject Classification ID

Nonparametric estimation (62G05) Markov processes: estimation; hidden Markov models (62M05) Diffusion processes (60J60)

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Nonparametric two-step estimation of drift function in the jump-diffusion model with noisy data ⋮ Adaptive confidence bands for Markov chains and diffusions: Estimating the invariant measure and the drift ⋮ Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions ⋮ Deviation inequalities for centered additive functionals of recurrent Harris processes having general state space ⋮ A two-step estimation of diffusion processes using noisy observations ⋮ Polynomial bounds in the Ergodic theorem for one-dimensional diffusions and integrability of hitting times

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