Lipschitz continuity of polyhedral Skorokhod maps
type: Item
instance of: scholarly article
title: Lipschitz continuity of polyhedral Skorokhod maps
zbMATH Open document ID: 1016.47048
DOI: 10.4171/ZAA/1047
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2002-07-22T00:00:00Z
review text: Summary: We show that a special stability condition of the associated system of oblique projections (the so-called \(\ell\)-paracontractivity) guarantees that the corresponding polyhedral Skorokhod problem in a Hilbert space \(X\) is solvable in the space of absolutely continuous functions with values in \(X\). If, moreover, the oblique projections are transversal, the solution exists and is unique for each continuous input and the Skorokhod map is Lipschitz continuous in both spaces \(C([0,T];X)\) and \(W^{1,1} (0,T;X)\). Also, an explicit upper bound for the Lipschitz constant is derived.
Mathematics Subject Classification ID: 47J40
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 52B70
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 1747392
zbMATH Keywords: oblique reflections
zbMATH Keywords: Lipschitz continuity
zbMATH Keywords: \(\ell\)-paracontractivity
zbMATH Keywords: polyhedral Skorokhod problem in Hilbert space
author: Pavel Krejč{í }
author: Alexander Vladimirov
MaRDI profile type: Publication
cites work: The stop operator related to a convex polyhedron
cites work: On lipschitz continuity of the solution mapping to the skorokhod problem, with applications
cites work: Convex duality and the Skorokhod problem. I
cites work: Norm conditions for convergence of infinite products
cites work: On the convergence of asynchronous paracontractions with application to tomographic reconstruction from incomplete data
cites work: Q3543379
cites work: Stability and paracontractivity of discrete linear inclusions
full work available at URL: https://doi.org/10.4171/zaa/1047
OpenAlex ID: W2077143197
description: scientific article; zbMATH DE number 1747392