Hitting probabilities for systems of non-linear stochastic heat equations with additive noise
Hitting probabilities for systems of non-linear stochastic heat equations with additive noise
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.
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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.Collections
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