Bessel-like processes and SDE
type: Item
instance of: scholarly article
title: Bessel-like processes and SDE
zbMATH Open document ID: 1088.60061
author: Ayako Yasue
published in: Journal of Mathematics of Kyoto University
publication date: 2006-03-09T00:00:00Z
review text: This paper deals with the Bessel-like prosess \(X_t\), which is the square root of \(Y_t\) described by the stochastic differential equation \(dY_t=2 \sqrt Y_tdB_t+b(Y_t)dt\), \(Y_t\geq 0\), where \(B_t\) is a Brownian motion and \(b\) is a continuous function with \(b(0)>0\). Though Itô's formula yields formally the stochastic differential equation \[ X_t=X_0+B_t+\int^t_0\frac{b(X^2_s)-1}{X_s} ds,\tag{*} \] this does not hold globally in time generally. Studying the behaviour of \(Y_t\) near the boundary point 0, the author presents a condition on \(b\), so that the stochastic differential equation (*) holds. Moreover, she obtains a new stochastic equation involving the local times, which holds for general \(b\).
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 31C25
zbMATH DE Number: 5010145
zbMATH Keywords: semimartingale
zbMATH Keywords: additive functional
zbMATH Keywords: bounded variation
zbMATH Keywords: local time
zbMATH Keywords: stochastic differential equation
reviewed by: Makiko Nisio
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250281699
OpenAlex ID: W1556531667
DOI: 10.1215/KJM/1250281699
description: scientific article; zbMATH DE number 5010145