A property of distributions of diffusion processes
type: Item
instance of: scholarly article
title: A property of distributions of diffusion processes
zbMATH Open document ID: 0826.60065
DOI: 10.1007/BF01209560
author: N. A. Tolmachev
published in: Mathematical Notes
publication date: 1994-11-16T00:00:00Z
review text: Let \(\mu_X\) be a distribution of the diffusion process defined by the equation \(dX_t = a(X_t) dW_t\), where \(a\) is a bounded analytic function. It is proved that there exists a set \(B\) in the space of trajectories \(C ([0,1])\) of complete \(\mu_X\)-measures such that for any \(y,h \in C ([0,1])\) the set on the line \(\{t : y + th \in B\}\) is at most countable. This means that \(\mu_X\) is located on the exceptional set in the Aronszajn sense.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60A10
zbMATH DE Number: 687509
zbMATH Keywords: diffusion process
zbMATH Keywords: analytic function
zbMATH Keywords: space of trajectories
zbMATH Keywords: exceptional set
reviewed by: R. Mikulevicius
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01209560
OpenAlex ID: W2059694714
description: scientific article; zbMATH DE number 687509