Intermittency properties in a hyperbolic Anderson model
Seminar Room 1, Newton Institute
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We study the asymptotics of the even moments of solutions to a stochastic wave equation in spatial dimension $3$ with linear multiplicative noise. 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, we also derive bounds on moments of the solution to the stochastic heat equation with linear multiplicative noise. This is joint work with Carl Mueller. It makes strong use of a Feynman-Kac type formula for moments of this stochastic wave equation developped in joint work with Carl Mueller and Roger Tribe.