  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, Hoffmann
and Rei{\ss} [Ann. Statist. 32 (2006), 2223-2253]. 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.
