Weighted sums of i.i.d. random variables attracted to integrals of stable processes (Q1092510)

Under the assumption of the convergence of partial sum processes \(Z_ n(t)\) of i.i.d. random variables to an \(\alpha\)-stable Lévy process \(Z_{(\alpha)}(t)\), \(0<\alpha \leq 2\), the convergence of weighted sums \(\int f_ n(u)dZ_ n(u)\) to \(\int f(u)dZ_{(\alpha)}(u)\) is studied. The general convergence result is then applied to examine the domain of attraction of the fractional stable process.