Nonstandard Construction of Levy Brownian Motion

摘要

A nonstandard construction of Levy Brownian motion on R sup d, which extends Anderson's nonstandard representation of Brownian motion, is presented. It involves a nonstandard construction of white noise and gives as a classical corollary a white noise integral representation of Levy Brownian motion. An invariance principle can be deduced in a similar way as Donsker's invariance principle follows from Anderson's construction.