Continuous dependence and time change for Ito equations
type: Item
instance of: scholarly article
title: Continuous dependence and time change for Ito equations
zbMATH Open document ID: 0535.60051
DOI: 10.1016/0022-0396(85)90001-4
published in: Journal of Differential Equations
publication date: 1985-01-01T00:00:00Z
review text: The paper concerns continuous dependence on the drift term and the invariants for Ito equations when a time change is performed. The continuity property with respect to drift terms is proved using a weaker topology than usually required and the distance between solutions is measured by the usual metric. For deterministic autonomous differential equations the invariant under a time change is the trajectory: in the case of Ito equations it is shown that such invariant is the set \(\overline{\cup_{t\leq 0}\sup p} P_ t(.)\), where \(P_ t(.)\) is the probability measure generated on \(R^ n\) by the random vector x(t,.). By an appropriate time change an Ito equation with unbounded coefficients can be transformed into one with bounded coefficients and this change gives an alternative way for extending to the case of unbounded coefficients the description of the above set as the attainable set of a deterministic control system.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 34F05
zbMATH DE Number: 3850203
zbMATH Keywords: invariants
zbMATH Keywords: time change
zbMATH Keywords: continuity property with respect to drift terms
author: Constantin Vârsan
MaRDI profile type: Publication
full work available at URL: 0022-0396(85)90001-4
OpenAlex ID: W2167282130
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description: scientific article; zbMATH DE number 3850203