Hitting Probabilities for Systems of Non-Linear Stochastic Heat Equations with Additive Noise

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dc.creatorDalang, Robert C.
dc.creatorKhoshnevisan, Davar
dc.creatorNualart, Eulalia
dc.date2007-02-23
dc.date.accessioned2026-07-07T07:48:30Z
dc.date.available2026-07-07T07:48:30Z
dc.descriptionWe 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 $\{u(t, x)\}_{t \in \mathbb{R}_+, x \in [0, 1]}$, in terms of respectively Hausdorff measure and Newtonian capacity. We also obtain the Hausdorff dimensions of level sets and their projections. A result of independent interest is an anisotropic form of the Kolmogorov continuity theorem.
dc.description44 pages; submitted for publication
dc.identifierhttps://arxiv.org/abs/math/0702710
dc.identifierhttp://arxiv.org/abs/math/0702710
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124522
dc.subjectProbability
dc.subjectPrimary: 60H15, 60J45; Secondary: 60G60
dc.titleHitting Probabilities for Systems of Non-Linear Stochastic Heat Equations with Additive Noise
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