A Lévy-type characterization of one-dimensional diffusions
type: Item
instance of: scholarly article
title: A Lévy-type characterization of one-dimensional diffusions
zbMATH Open document ID: 0901.60050
author: Michael Voit
published in: Archiv der Mathematik
publication date: 1998-06-23T00:00:00Z
review text: The author gives a Lévy-type characterization for a one-dimensional time-homogeneous diffusion process \(X\), associated with the second-order differential operator \(L\). One introduces the scale function \(p\), such that \(Lp=0\) and the variance function \(s\), such that \(Ls=1\). These functions are defined in terms of the diffusion function and the drift function of \(X\). Then, one proves that \(X\) is a diffusion associated with \(L\) if and only if the processes \((p(X_{t}))_{t\geq 0}\) and \((s(X_{t})-t)_{t\geq 0}\) are local martingales.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 1145761
zbMATH Keywords: diffusion process
zbMATH Keywords: local martingale
reviewed by: Mihai Gradinaru
MaRDI profile type: Publication
full work available at URL: s000130050189
OpenAlex ID: W2059337814
DOI: 10.1007/S000130050189
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description: scientific article; zbMATH DE number 1145761