The non-linear sewing lemma III: Stability and generic properties
Author
dc.contributor.author
Brault, Antoine
Author
dc.contributor.author
Lejay, Antoine
Admission date
dc.date.accessioned
2020-11-11T22:46:24Z
Available date
dc.date.available
2020-11-11T22:46:24Z
Publication date
dc.date.issued
2020
Cita de ítem
dc.identifier.citation
Forum Mathematicum Volumen: 32 Número: 5 Páginas: 1177-1197 Sep 2020
es_ES
Identifier
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10.1515/forum-2019-0309
Identifier
dc.identifier.uri
https://repositorio.uchile.cl/handle/2250/177672
Abstract
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Solutions of Rough Differential Equations (RDE) may be defined as paths whose increments are close to an approximation of the associated flow. They are constructed through a discrete scheme using a non-linear sewing lemma. In this article, we show that such solutions also solve a fixed point problem by exhibiting a suitable functional. Convergence then follows from consistency and stability, two notions that are adapted to our framework. In addition, we show that uniqueness and convergence of discrete approximations is a generic property, meaning that it holds excepted for a set of vector fields and starting points which is of Baire first category. At last, we show that Brownian flows are almost surely unique solutions to RDE associated to Lipschitz flows. The later property yields almost sure convergence of Milstein schemes.
es_ES
Patrocinador
dc.description.sponsorship
Center for Mathematical Modeling, Conicyt
AFB 170001