Additive functionals as rough paths
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2685 | |
dc.contributor.author | Deuschel, Jean-Dominique | |
dc.contributor.author | Orenshtein, Tal | |
dc.contributor.author | Perkowski, Nicolas | |
dc.date.accessioned | 2022-06-30T12:42:34Z | |
dc.date.available | 2022-06-30T12:42:34Z | |
dc.date.issued | 2020 | |
dc.description.abstract | We consider additive functionals of stationary Markov processes and show that under Kipnis--Varadhan type conditions they converge in rough path topology to a Stratonovich Brownian motion, with a correction to the Lévy area that can be described in terms of the asymmetry (non-reversibility) of the underlying Markov process. We apply this abstract result to three model problems: First we study random walks with random conductances under the annealed law. If we consider the Itô rough path, then we see a correction to the iterated integrals even though the underlying Markov process is reversible. If we consider the Stratonovich rough path, then there is no correction. The second example is a non-reversible Ornstein-Uhlenbeck process, while the last example is a diffusion in a periodic environment. As a technical step we prove an estimate for the p-variation of stochastic integrals with respect to martingales that can be viewed as an extension of the rough path Burkholder-Davis-Gundy inequality for local martingale rough paths of [FV08], [CF19] and [FZ18] to the case where only the integrator is a local martingale. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9335 | |
dc.identifier.uri | https://doi.org/10.34657/8373 | |
dc.language.iso | eng | |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2685 | |
dc.relation.hasversion | https://doi.org/10.1214/20-AOP1488 | |
dc.relation.issn | 2198-5855 | |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | |
dc.subject.other | Rough paths | eng |
dc.subject.other | invariance principles in the rough | eng |
dc.subject.other | path topology | eng |
dc.subject.other | additive functionals of Markov processes | eng |
dc.subject.other | Kipnis--Varadhan theory | eng |
dc.subject.other | homogenization | eng |
dc.subject.other | random conductance model | eng |
dc.subject.other | random walks with random conductances | eng |
dc.title | Additive functionals as rough paths | eng |
dc.type | Report | eng |
dc.type | Text | eng |
dcterms.extent | 31 S. | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Mathematik | |
wgl.type | Report / Forschungsbericht / Arbeitspapier |
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