Localization results for densities associated with stable small-noise diffusions
type: Item
instance of: scholarly article
title: Localization results for densities associated with stable small-noise diffusions
zbMATH Open document ID: 0621.60061
DOI: 10.1007/BF00319299
author: Martin V. Day
publication date: 1988-01-01T00:00:00Z
review text: This paper concerns asymptotic properties of the stationary density associated with small-noise diffusion processes, such as considered in the well-known work of \textit{A. D. Ventcel} and \textit{M. I. Frejdlin} [Usp. Mat. Nauk 25, No.1(151), 3-55 (1970; Zbl 0291.34042); English translation in Russ. Math. Surv. 25, 1-55 (1970)]. We assume that the origin is a globally attracting asymptotically stable equilibrium point of the underlying deterministic flow. For a bounded domain D, containing the origin, we derive estimates which establish the asymptotic independence, as the size of the noise vanishes, of the equilibrium density in D from the coefficients of the process outside D. These results are applied to generalize a result of \textit{S.-Y. Sheu} [SIAM J. Math. Anal. 17, 451-460 (1986; Zbl 0599.60073)] on an asymptotic representation of the equilibrium density.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 4007373
zbMATH Keywords: localization results for densities
zbMATH Keywords: stable small-noise diffusions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00319299
OpenAlex ID: W2000941187
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4007373