An action functional for Lévy Brownian motion
The author uses \textit{A. Stoll}'s [Probab. Theory Relat. Fields 71, 321- 334 (1986; Zbl 0562.60086)] construction of Lévy Brownian motion \(\ell\) on \({\mathbb{R}}^ d\) as a white noise integral to obtain an action functional I(x) defined on the `surface' x of \(\ell\). From this, he obtains a Cameron-Martin formula for translation of Lévy measure \(\lambda\). Further, a large deviation principle for scaled Lévy measures \(\lambda_{\delta}\) is obtained. The author works in a Robinson-styled \(\omega_ 1\)-saturated nonstandard universe to obtain these results as well as many others. This paper shows, once again, how intuitively superior nonstandard techniques are when attacking problems of this type.
scientific article; zbMATH DE number 4155642
scientific article