One-dimensional bi-generalized diffusion processes
type: Item
instance of: scholarly article
title: One-dimensional bi-generalized diffusion processes
zbMATH Open document ID: 0701.60078
author: Yukio Ogura
published in: Journal of the Mathematical Society of Japan
publication date: 1989-01-01T00:00:00Z
review text: The notion of one-dimensional diffusion or gap diffusion is generalised by allowing the scale function s to have flats, i.e. s is (only) non- decreasing. Using the function s and a non-negative speed measure m an analytical construction of a Markov process X - called bi-generalised diffusion process (BGDP) - is given. It is seen that X does not have in general the strong Markov property and right continuous paths. In fact, sample paths are described using a gap diffusion when X is off the flats of s and a stationary process when in the flats. Moreover, conditions for the convergence of finite-dimensional distributions in a sequence of BGDP's are given. These results are used to study metastable behaviour in statistical physics, asymptotic behaviour of a diffusion in random environment and approximations of diffusion processes of gene frequencies. Consequences of the existence of bi-generalised birth and death processes for the Stieltjes' moment problem are also discussed.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 4149307
zbMATH Keywords: random media
zbMATH Keywords: strong Markov property
zbMATH Keywords: stationary process
zbMATH Keywords: statistical physics
zbMATH Keywords: asymptotic behaviour of a diffusion in random environment
zbMATH Keywords: Stieltjes' moment problem
reviewed by: Paavo Salminen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04120213
OpenAlex ID: W2052438464
DOI: 10.2969/JMSJ/04120213
description: scientific article; zbMATH DE number 4149307