Diffusions with singular drift related to wave functions
type: Item
instance of: scholarly article
title: Diffusions with singular drift related to wave functions
zbMATH Open document ID: 0791.60066
DOI: 10.1007/BF01195885
author: Robert Aebi
publication date: 1994-07-07T00:00:00Z
review text: Schrödinger equations are equivalent to pairs of mutually time-reversed nonlinear diffusion equations. Here the associated diffusion processes with singular drift are constructed under assumptions adopted from the theory of Schrödinger operators, expressed in terms of a local space- time Sobolev space. By means of Nagasawa's multiplicative functional \(N^ t_ s\), a Radon-Nikodym derivative on the space of continuous paths, a transformed process is obtained from Wiener measure. Its singular drift is identified by Maruyama's drift transformation. For this a version of Itô's formula for continuous space-time functions with first and second order derivatives in the sense of distributions satisfying local integrability conditions has to be derived. The equivalence is shown between weak solutions of a diffusion equation with singular creation and killing term and the solution of a Feynman-Kac integral equation with a locally integrable potential function.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 60J70
zbMATH DE Number: 569070
zbMATH Keywords: Schrödinger equations
zbMATH Keywords: Nagasawa's multiplicative functional
zbMATH Keywords: Wiener measure
zbMATH Keywords: Maruyama's drift transformation
zbMATH Keywords: diffusion equation with singular creation and killing term
zbMATH Keywords: Feynman-Kac integral
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 569070