A nonstandard construction of Lévy Brownian motion (Q1057004)

A nonstandard construction of Lévy Brownian motion on \({\mathbb{R}}^ d\) is presented, which extends \textit{R. M. Anderson's} nonstandard representation of Brownian motion [Isr. J. Math. 25, 15-46 (1976; Zbl 0353.60052)]. It involves a nonstandard construction of white noise and gives as a classical corollary a new white noise integral representation of Lévy Brownian motion. Moreover, a new invariance principle can be deduced in a similar way as Donsker's invariance principle follows from Anderson's construction.