Wavelet estimation in diffusions with periodicity

Michael Diether ()

Statistical Inference for Stochastic Processes, 2012, vol. 15, issue 3, 257-284

Abstract: We consider a time-inhomogeneous diffusion process, whose drift term contains a deterministic T-periodic signal with known periodicity. This signal is supposed to be contained in a Besov space, we try to estimate it using a non-parametric wavelet estimator. Our estimator is inspired by the thresholded wavelet density estimator constructed by Donoho, Johnstone, Kerkyacharian and Picard in 1996. Under certain ergodicity assumptions to the process, we can give the same asymptotic rate of convergence as for the density estimator. Copyright Springer Science+Business Media Dordrecht 2012

Keywords: Diffusions; Periodic drift; Estimation of unknown signal; Wavelet estimator; Nonparametric rate of convergence; Markov chain; Moment inequality; Exponential inequality; 62G05; 62G20; 62M05 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s11203-012-9070-x

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