Hitting probabilities for systems of non-linear stochastic heat equations with additive noise
By Robert C. Dalang, Davar Khoshnevisan, E. Nualart. 2007
97 citations recorded by the source corpus.
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 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.
Subfields: Finance, Mathematical Physics, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/78b1fc2c04c7fca6b9c72f822e90131b5688b598
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Citations in the corpus
- Moments and growth indices for the nonlinear stochastic heat equation with rough initial conditions (2013, background): “…Statistics, 2015 MOMENTS AND GROWTH INDICES FOR THE NONLINEAR STOCHASTIC HEAT EQUATION WITH ROUGH INITIAL CONDITIONS1 BY LE CHEN AND ROBERT C. DALANG École Polytechnique Fédérale de Lausanne We study the nonlinear stochastic heat equation in the spatial domain R, driven by space–time white noise.”
- Hölder-continuity for the nonlinear stochastic heat equation with rough initial conditions (2013, unknown): “Finally, in the papers [11,12], Dalang et al.”