DC Field | Value | Language |
---|---|---|
dc.contributor.author | Le Chen | - |
dc.contributor.author | Jingyu Huang | - |
dc.contributor.author | Davar Khoshnevisan | - |
dc.contributor.author | KIM, KUNWOO | - |
dc.date.accessioned | 2019-11-14T00:30:03Z | - |
dc.date.available | 2019-11-14T00:30:03Z | - |
dc.date.created | 2019-11-13 | - |
dc.date.issued | 2019-10 | - |
dc.identifier.issn | 1083-6489 | - |
dc.identifier.uri | https://oasis.postech.ac.kr/handle/2014.oak/99875 | - |
dc.description.abstract | The 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∈R3logE(|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.language | English | - |
dc.publisher | Institute of Mathematical Statistics | - |
dc.relation.isPartOf | Electronic Journal of Probability | - |
dc.title | Dense blowup for parabolic SPDEs | - |
dc.type | Article | - |
dc.identifier.doi | 10.1214/19-EJP372 | - |
dc.type.rims | ART | - |
dc.identifier.bibliographicCitation | Electronic Journal of Probability, v.24, no.118, pp.1 - 33 | - |
dc.identifier.wosid | 000493105700001 | - |
dc.citation.endPage | 33 | - |
dc.citation.number | 118 | - |
dc.citation.startPage | 1 | - |
dc.citation.title | Electronic Journal of Probability | - |
dc.citation.volume | 24 | - |
dc.contributor.affiliatedAuthor | KIM, KUNWOO | - |
dc.identifier.scopusid | 2-s2.0-85074500133 | - |
dc.description.journalClass | 1 | - |
dc.description.journalClass | 1 | - |
dc.description.isOpenAccess | Y | - |
dc.type.docType | Article | - |
dc.subject.keywordPlus | STOCHASTIC HEAT-EQUATION | - |
dc.subject.keywordPlus | REGULARITY | - |
dc.subject.keywordPlus | DRIVEN | - |
dc.subject.keywordPlus | NOISE | - |
dc.subject.keywordAuthor | stochastic partial differential equations | - |
dc.subject.keywordAuthor | blowup | - |
dc.subject.keywordAuthor | intermittency | - |
dc.relation.journalWebOfScienceCategory | Statistics & Probability | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
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