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dc.contributor.authorAttouchi, Amal
dc.contributor.authorLuiro, Hannes
dc.contributor.authorParviainen, Mikko
dc.date.accessioned2021-10-01T07:12:15Z
dc.date.available2021-10-01T07:12:15Z
dc.date.issued2021
dc.identifier.citationAttouchi, A., Luiro, H., & Parviainen, M. (2021). Gradient and Lipschitz Estimates for Tug-of-War Type Games. <i>SIAM Journal on Mathematical Analysis</i>, <i>53</i>(2), 1295-1319. <a href="https://doi.org/10.1137/19M1256816" target="_blank">https://doi.org/10.1137/19M1256816</a>
dc.identifier.otherCONVID_68758290
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/77975
dc.description.abstractWe define a random step size tug-of-war game and show that the gradient of a value function exists almost everywhere. We also prove that the gradients of value functions are uniformly bounded and converge weakly to the gradient of the corresponding $p$-harmonic function. Moreover, we establish an improved Lipschitz estimate when boundary values are close to a plane. Such estimates are known to play a key role in the higher regularity theory of partial differential equations. The proofs are based on cancellation and coupling methods as well as an improved version of the cylinder walk argument.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherSociety for Industrial and Applied Mathematics
dc.relation.ispartofseriesSIAM Journal on Mathematical Analysis
dc.rightsIn Copyright
dc.subject.othergradient regularity
dc.subject.otherLipschitz estimate
dc.subject.otherp-Laplace
dc.subject.otherstochastic two player zero-sum game
dc.subject.othertug-of-war with noise
dc.titleGradient and Lipschitz Estimates for Tug-of-War Type Games
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202110015038
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineAnalyysin ja dynamiikan tutkimuksen huippuyksikköfi
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineAnalysis and Dynamics Research (Centre of Excellence)en
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.description.reviewstatuspeerReviewed
dc.format.pagerange1295-1319
dc.relation.issn0036-1410
dc.relation.numberinseries2
dc.relation.volume53
dc.type.versionacceptedVersion
dc.rights.copyright© 2021, Society for Industrial and Applied Mathematics
dc.rights.accesslevelopenAccessfi
dc.subject.ysopeliteoria
dc.subject.ysostokastiset prosessit
dc.subject.ysoosittaisdifferentiaaliyhtälöt
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p13476
jyx.subject.urihttp://www.yso.fi/onto/yso/p11400
jyx.subject.urihttp://www.yso.fi/onto/yso/p12392
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.1137/19M1256816


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