ON THE FOURIER COEFFICIENTS OF LINEAR FRACTIONAL STABLE MOTION

Inspired by a theorem of Marcinkiewicz [J. Marcinkiewicz, On a class of functions and their Fourier series, C. R. Soc. Sci. Varsovie, 26: 71-77, 1934. Reprinted in: J. Marcinkiewicz, Collected Papers (A. Zygmund (Ed.)), Panstwowe Wydawnictwo Naukowe, Warsaw, 1964] stating that the maximum of the absolute values of real Fourier coefficients a(n) and b(n) of a function of bounded p-variation (p >= 1) on an interval [0, 1] is of order O(n(-1/p)) as n -> infinity, we compute the Fourier coefficients of the linear fractional stable motion (LFSM) and of the closely related Riemann-Liouville (RL) process and investigate the rate of their decay.