Positivity of the density for the stochastic wave equation in two spatial dimensions
ESAIM: Probability and Statistics, Tome 7 (2003) , pp. 89-114.

We consider the random vector u(t,x ̲)=(u(t,x 1 ),,u(t,x d )), where t>0,x 1 ,,x d are distinct points of 2 and u denotes the stochastic process solution to a stochastic wave equation driven by a noise white in time and correlated in space. In a recent paper by Millet and Sanz-Solé [10], sufficient conditions are given ensuring existence and smoothness of density for u(t,x ̲). We study here the positivity of such density. Using techniques developped in [1] (see also [9]) based on Analysis on an abstract Wiener space, we characterize the set of points y d where the density is positive and we prove that, under suitable assumptions, this set is d .

DOI : https://doi.org/10.1051/ps:2003002
Classification : 60H15,  60H07
Mots clés : stochastic partial differential equations, Malliavin calculus, wave equation, probability densities
@article{PS_2003__7__89_0,
     author = {Chaleyat-Maurel, Mireille and Sanz-Sol\'e, Marta},
     title = {Positivity of the density for the stochastic wave equation in two spatial dimensions},
     journal = {ESAIM: Probability and Statistics},
     pages = {89--114},
     publisher = {EDP-Sciences},
     volume = {7},
     year = {2003},
     doi = {10.1051/ps:2003002},
     zbl = {1021.60049},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps:2003002/}
}
Chaleyat-Maurel, Mireille; Sanz-Solé, Marta. Positivity of the density for the stochastic wave equation in two spatial dimensions. ESAIM: Probability and Statistics, Tome 7 (2003) , pp. 89-114. doi : 10.1051/ps:2003002. http://www.numdam.org/articles/10.1051/ps:2003002/

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