Spectral estimation for diffusions with random sampling times

Jakub Chorowski and Mathias Trabs

Stochastic Processes and their Applications, 2016, vol. 126, issue 10, 2976-3008

Abstract: The nonparametric estimation of the volatility and the drift coefficient of a scalar diffusion is studied when the process is observed at random time points. The constructed estimator generalizes the spectral method by Gobet et al. (2006). The estimation procedure is optimal in the minimax sense and adaptive with respect to the sampling time distribution and the regularity of the coefficients. The proofs are based on the eigenvalue problem for the generalized transition operator. The finite sample performance is illustrated in a numerical example.

Keywords: Ergodic diffusion processes; Generalized transition operator; Lepski’s method; Minimax optimal convergence rates; Nonparametric estimation; Random sampling (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spa.2016.03.009

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