The Donsker's Theorem for Levy Stable Motions via Mallows Distance

#### C.C.Y. Dorea, M.A. Oliveira

2014, v.20, Issue 1, 167-172

ABSTRACT

The $\alpha$-stable Levy motions have stationary independent increments and possess self-similarity properties leading to a role among stable processes similar to the role that Brownian motion plays among Gaussian processes. In this note, making use of the Mallows distance and for $1<\alpha \leq 2$, we derive the classical Donsker's theorem for $\alpha$-stable Levy motions.

Keywords: Donsker's theorem,Mallows distance,stable laws