On Lipschitz dependence in systems with differentiated inputs
type: Item
instance of: scholarly article
title: On Lipschitz dependence in systems with differentiated inputs
zbMATH Open document ID: 0553.60054
DOI: 10.1007/BF01450568
published in: Mathematische Annalen
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164010
review text: An extension [given by a representation of \textit{H. Doss}, Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. B 13, 99-125 (1977; Zbl 0359.60087), and \textit{H. J. Sussmann}, Ann. Probab. 6, 19-41 (1978; Zbl 0391.60056)] of the mapping \(z\to x\), \(\dot x=f(x)+G(x)\dot z\), to \(z\in L^{\infty}([0,1])\) is considered. Results on its (local) Lipschitz continuity (w.r to \(L^ p\)-norms (p\(\leq \infty)\), and Skorokhod-type metrics) as well as estimates on its local Lipschitz coefficients are obtained. These estimates are used to investigate preservation of convergence rates under the mapping \(z\to x\) in case of random inputs z which are large with small probability, and to obtain rate-of-convergence estimates of some approximate solutions of stochastic differential equations.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 3881603
zbMATH Keywords: Lipschitz continuity
zbMATH Keywords: Skorokhod-type metrics
zbMATH Keywords: preservation of convergence rates
author: Werner Römisch
author: Anton Wakolbinger
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3881603