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dc.contributor.authorLe Chen-
dc.contributor.authorJingyu Huang-
dc.contributor.authorDavar Khoshnevisan-
dc.contributor.authorKIM, KUNWOO-
dc.date.available2019-11-14T00:30:03Z-
dc.date.created2019-11-13-
dc.date.issued2019-10-
dc.identifier.issn1083-6489-
dc.identifier.urihttp://oasis.postech.ac.kr/handle/2014.oak/99875-
dc.description.abstractThe main result of this paper is that there are examples of stochastic partial differential equations [hereforth, SPDEs] of the type ∂tu=12Δu+σ(u)ηon (0,∞)×R3 ∂tu=12Δu+σ(u)ηon (0,∞)×R3 such that the solution exists and is unique as a random field in the sense of Dalang [6] and Walsh [31], yet the solution has unbounded oscillations in every open neighborhood of every space-time point. We are not aware of the existence of such a construction in spatial dimensions below 33. En route, it will be proved that when σ(u)=uσ(u)=u there exist a large family of parabolic SPDEs whose moment Lyapunov exponents grow at least sub exponentially in its order parameter in the sense that there exist A1,β∈(0,1)A1,β∈(0,1) such that γ––(k):=lim inft→∞t−1infx∈R3logE(|u(t,x)|k)⩾A1exp(A1kβ)for all k⩾2. γ_(k):=lim inft→∞t−1infx∈R3log⁡E(|u(t,x)|k)⩾A1exp⁡(A1kβ)for all k⩾2. This sort of “super intermittency” is combined with a local linearization of the solution, and with techniques from Gaussian analysis in order to establish the unbounded oscillations of the sample functions of the solution to our SPDE.-
dc.languageEnglish-
dc.publisherInstitute of Mathematical Statistics-
dc.titleDense blowup for parabolic SPDEs-
dc.typeArticle-
dc.type.rimsART-
dc.identifier.bibliographicCitationElectronic Journal of Probability, v.24, no.118, pp.1 - 33-
dc.identifier.wosid000493105700001-
dc.citation.endPage33-
dc.citation.number118-
dc.citation.startPage1-
dc.citation.titleElectronic Journal of Probability-
dc.citation.volume24-
dc.contributor.affiliatedAuthorKIM, KUNWOO-
dc.identifier.scopusid2-s2.0-85074500133-
dc.description.journalClass1-
dc.description.isOpenAccessY-
dc.type.docTypeArticle-
dc.subject.keywordAuthorstochastic partial differential equations-
dc.subject.keywordAuthorblowup-
dc.subject.keywordAuthorintermittency-

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Dept of Mathematics
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