Mixed fractional Brownian motion: A spectral take

This paper provides yet another look at the mixed fractional Brownian motion (fBm), this time, from the spectral perspective. The main result is an asymptotic approximation for the eigenvalues of its covariance operator. Using this approximation we derive the exact asymptotics of the L₂-small ball probabilities, which was previously known only with logarithmic accuracy. The obtained expression exhibits an interesting stratification of scales, which occurs at certain values of the Hurst parameter of the fractional component. Some of them have been previously encountered in other problems involving such mixtures.