Level sets of the stochastic wave equation driven by a symmetric Lévy noise

Khoshnevisan, Davar; Nualart, Eulalia

Bernoulli, Tome 14 (2008) no. 1, p. 899-925 / Harvested from Project Euclid

Résumé

We consider the solution {u(t, x); t≥0, x∈R} of a system of d linear stochastic wave equations driven by a d-dimensional symmetric space-time Lévy noise. We provide a necessary and sufficient condition on the characteristic exponent of the Lévy noise, which describes exactly when the zero set of u is non-void. We also compute the Hausdorff dimension of that zero set when it is non-empty. These results will follow from more general potential-theoretic theorems on the level sets of Lévy sheets.

Publié le : 2008-11-15
Classification: level sets, Lévy noise, potential theory, stochastic wave equation

@article{1225980564,
     author = {Khoshnevisan, Davar and Nualart, Eulalia},
     title = {Level sets of the stochastic wave equation driven by a symmetric L\'evy noise},
     journal = {Bernoulli},
     volume = {14},
     number = {1},
     year = {2008},
     pages = { 899-925},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1225980564}
}

Khoshnevisan, Davar; Nualart, Eulalia. Level sets of the stochastic wave equation driven by a symmetric Lévy noise. Bernoulli, Tome 14 (2008) no. 1, pp.  899-925. http://gdmltest.u-ga.fr/item/1225980564/