Maximum likelihood drift estimation for a threshold diffusion
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2497 | |
dc.contributor.author | Lejay, Antoine | |
dc.contributor.author | Pigato, Paolo | |
dc.date.accessioned | 2018-04-16T09:58:00Z | |
dc.date.available | 2019-06-28T08:17:20Z | |
dc.date.issued | 2018 | |
dc.description.abstract | We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold diffusion is called the drifted Oscillating Brownian motion. The asymptotic behaviors of the positive and negative occupation times rule the ones of the estimators. Differently from most known results in the literature, we do not restrict ourselves to the ergodic framework: indeed, depending on the signs of the drift, the process may be ergodic, transient or null recurrent. For each regime, we establish whether or not the estimators are consistent; if they are, we prove the convergence in long time of the properly rescaled difference of the estimators towards a normal or mixed normal distribution. These theoretical results are backed by numerical simulations. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2647 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/3122 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2497 | |
dc.relation.issn | 2198-5855 | eng |
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 | eng |
dc.subject.other | Threshold diffusion | eng |
dc.subject.other | oscillating Brownian motion | eng |
dc.subject.other | maximum likelihood estimator | eng |
dc.subject.other | null recurrent process | eng |
dc.subject.other | ergodic process | eng |
dc.subject.other | transient process | eng |
dc.subject.other | mixed normal distribution | eng |
dc.title | Maximum likelihood drift estimation for a threshold diffusion | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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