Convergence of Certain Functionals of Integral Fractional Processes

Abstract

In this paper we consider the asymptotic behavior of functionals of processes of the form a << (0) (t) u (s) dB (s) (H) , where B (H) is a fractional Brownian motion with Hurst parameter H, and u is a process with finite q-variation, q < 1/(1-H). We establish the stable convergence of the corresponding fluctuations.