Hitting probabilities for systems of non-linear stochastic heat equations with additive noise
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- dc.contributor.author Dalang, Robert C.
- dc.contributor.author Khoshnevisan, Davar
- dc.contributor.author Nualart, Eulàlia
- dc.date.accessioned 2020-03-20T08:49:07Z
- dc.date.available 2020-03-20T08:49:07Z
- dc.date.issued 2007
- dc.description.abstract We consider a system of d coupled non-linear stochastic heat equations in spatial dimension 1 driven by d-dimensional additive space-time white noise. We establish upper and lower bounds on hitting probabilities of the solution {u(t, x)}t∈R+, x∈[0 ,1], in terms of respectively Hausdorff measure and Newtonian capacity. We determine the Hausdorff dimensions of level sets and their projections. We also present an anisotropic form of the Kolmogorov continuity theorem.
- dc.format.mimetype application/pdf
- dc.identifier.citation Dalang RC, Khoshnevisan D, Nualart E. Hitting probabilities for systems of non-linear stochastic heat equations with additive noise. ALEA Lat Am J Probab Math Stat. 2007;3:231-71.
- dc.identifier.issn 1980-0436
- dc.identifier.uri http://hdl.handle.net/10230/43973
- dc.language.iso eng
- dc.publisher ALEA
- dc.relation.ispartof ALEA Latin American Journal of Probability and Mathematical Statistics. 2007;3:231-71.
- dc.rights © ALEA. Published at: http://alea.impa.br/english/index_v3.htm
- dc.rights.accessRights info:eu-repo/semantics/openAccess
- dc.subject.keyword Hitting probabilities
- dc.subject.keyword Systems of non-linear stochastic heat equations
- dc.subject.keyword Space-time white noise
- dc.subject.keyword Capacity
- dc.subject.keyword Hausdorff measure
- dc.subject.keyword Anisotropic Kolmogorov continuity theorem
- dc.title Hitting probabilities for systems of non-linear stochastic heat equations with additive noise
- dc.type info:eu-repo/semantics/article
- dc.type.version info:eu-repo/semantics/publishedVersion