George Deligiannidis

Asymptotic variance of the self-intersections of stable random walks using Darboux-Wiener theory

We present a Darboux-Wiener type lemma as a powerful alternative to the classical Tauberian theorem when monotonicity is not known a priori. We apply it to obtain the exact asymptotics of the variance of the self-intersections of a one-dimensional stable random walk. Finally we prove a functional central limit theorem for stable random walk in random scenery conjectured in [1].

Variance of partial sums of stationary sequences

Let X1,X2,… be a centred sequence of weakly stationary random variables with spectral measure F and partial sums Sn=X1+⋯+Xn. We show that var(Sn) is regularly varying of index γ at infinity, if and only if G(x):=∫x−xF(dx) is regularly varying of index 2−γ at the origin (0