Browsing Articles (Departament d'Economia) by Subject "Capacity"

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Critical Brownian sheet does not have double points

Dalang, Robert C.; Khoshnevisan, Davar; Nualart, Eulàlia; Wu, Dongsheng; Xiao, Yimin (Institute of Mathematical Statistics (IMS), 2012)

We derive a decoupling formula for the Brownian sheet which has the following ready consequence: An N-parameter Brownian sheet in Rd has double points if and only if d<4N. In particular, in the critical case where d=4N, ...
Hitting probabilities for systems of non-linear stochastic heat equations with additive noise

Dalang, Robert C.; Khoshnevisan, Davar; Nualart, Eulàlia (ALEA, 2007)

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 ...

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