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.)), PaństwoweWydawnictwo Naukowe,Warsaw, 1964] stating that the maximum of the absolute values of real Fourier coefficients a and b of a function of bounded p-variation $$ \left( {p \geqslant 1} \right) $$ on an interval [0 , 1] is of order O( n) as n → ∞, 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. [ABSTRACT FROM AUTHOR]