An action functional for Lévy Brownian motion
type: Item
instance of: scholarly article
title: An action functional for Lévy Brownian motion
zbMATH Open document ID: 0704.60107
DOI: 10.1007/BF00049129
author: Nigel J. Cutland
published in: Acta Applicandae Mathematicae
publication date: 1990-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60K99
Mathematics Subject Classification ID: 03H05
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 26E05
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 4155642
zbMATH Keywords: Loeb measure
zbMATH Keywords: Lévy Brownian motion
zbMATH Keywords: Cameron-Martin formula
zbMATH Keywords: translation of Lévy measure
zbMATH Keywords: nonstandard techniques
MaRDI profile type: Publication
cites work: Q3742397
cites work: Infinitesimals in Action
cites work: Nonstandard Measure Theory and its Applications
cites work: Q3807204
cites work: Q3872705
cites work: A nonstandard construction of Lévy Brownian motion
cites work: An introduction to the theory of large deviations
description: scientific article; zbMATH DE number 4155642