Extending martingale measure stochastic integral with applications to spatially homogeneous S. P. D. E's.
The non-linear stochastic wave equation in high dimensions.
Some non-linear s. p. d. e's that are second order in time.
Sur l'arrêt optimal de processus à temps multidimensionnel continu
Correction : «Sur l'arrêt optimal de processus à temps multidimensionnel continu»
Intermittency properties in a hyperbolic Anderson problem
We study the asymptotics of the even moments of solutions to a stochastic wave equation in spatial dimension 3 with linear multiplicative spatially homogeneous gaussian noise that is white in time. Our main theorem states that these moments grow more quickly than one might expect. This phenomenon is well known for parabolic stochastic partial differential equations, under the name of intermittency. Our results seem to be the first example of this phenomenon for hyperbolic equations. For comparison,...
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