Diffusions as a limit of stretched Brownian motions
type: Item
instance of: scholarly article
title: Diffusions as a limit of stretched Brownian motions
zbMATH Open document ID: 0542.60079
DOI: 10.1016/0001-8708(83)90070-1
author: James K. Brooks
author: R. Chacón
published in: Advances in Mathematics
publication date: 1983-01-01T00:00:00Z
review text: The authors show that any regular diffusion on the line can be written as a weak limit of a class of processes called stretched Brownian motions. These are diffusions whose scale functions are piecewise-linear and whose speed measures have densities which are step-functions. The canonical example of such a process is the skew Brownian motion described in the book of \textit{K. Itô} and \textit{H. P. McKean}, Diffusion processes and their sample paths. (1965; Zbl 0127.095), 2nd corrected printing 1974. The stretched Brownian motions are in turn shown to be weak limits of certain random walks.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 3862185
zbMATH Keywords: stretched Brownian motions
zbMATH Keywords: skew Brownian motion
zbMATH Keywords: weak limits of certain random walks
MaRDI profile type: Publication
full work available at URL: 0001-8708(83)90070-1
OpenAlex ID: W2092817862
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description: scientific article; zbMATH DE number 3862185