Dalang, Robert C.Khoshnevisan, DavarNualart, Eulàlia2020-03-202020-03-202007Dalang 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;3:231-71.1980-0436http://hdl.handle.net/10230/43973We 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.application/pdfeng© ALEA. Published at: http://alea.impa.br/english/index_v3.htminfo:eu-repo/semantics/articleHitting probabilitiesSystems of non-linear stochastic heat equationsSpace-time white noiseCapacityHausdorff measureAnisotropic Kolmogorov continuity theoreminfo:eu-repo/semantics/openAccess