Existence and uniqueness of solutions of stochastic functional differential equations
| dc.contributor.author | Renesse, Max-K. von | |
| dc.contributor.author | Scheutzow, Michael | |
| dc.date.accessioned | 2017-11-30T10:20:05Z | |
| dc.date.available | 2017-11-30T10:20:05Z | |
| dc.date.issued | 2010 | |
| dc.description | Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich. | de |
| dc.description | This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively. | en |
| dc.description.abstract | Using a variant of the Euler–Maruyama scheme for stochastic functional differential equations with bounded memory driven by Brownian motion we show that only weak one-sided local Lipschitz (or “monotonicity”) conditions are sufficient for local existence and uniqueness of strong solutions. In case of explosion the method yields the maximal solution up to the explosion time. We also provide a weak growth condition which prevents explosions to occur. In an appendix we formulate and prove four lemmas which may be of independent interest: three of them can be viewed as rather general stochastic versions of Gronwall's Lemma, the final one provides tail bounds for Hölder norms of stochastic integrals. | en |
| dc.description.sponsorship | DFG, FOR 718, Analysis and stochastics in complex physical systems | en |
| dc.identifier.eissn | 1569-397X | |
| dc.identifier.issn | 0926-6364 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/7235 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-6511 | |
| dc.language.iso | en | |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
| dc.subject.ddc | 510 Mathematik | |
| dc.subject.other | stochastic functional differential equation | en |
| dc.subject.other | existence of solution | en |
| dc.subject.other | maximal solution | en |
| dc.subject.other | uniqueness of solution | en |
| dc.subject.other | Dereich lemma | en |
| dc.subject.other | stochastic Gronwall lemma | en |
| dc.title | Existence and uniqueness of solutions of stochastic functional differential equations | en |
| dc.type | Article | |
| dc.type.version | publishedVersion | |
| dcterms.bibliographicCitation.doi | 10.1515/rose.2010.015 | |
| dcterms.bibliographicCitation.issue | 3 | |
| dcterms.bibliographicCitation.journaltitle | Random operators and stochastic equations | |
| dcterms.bibliographicCitation.originalpublishername | De Gruyter | |
| dcterms.bibliographicCitation.originalpublisherplace | Berlin [u.a.] | |
| dcterms.bibliographicCitation.pageend | 284 | |
| dcterms.bibliographicCitation.pagestart | 267 | |
| dcterms.bibliographicCitation.volume | 18 | |
| tub.accessrights.dnb | domain | |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Stochastische Analysis | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.group | FG Stochastische Analysis | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin |
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