Wave Equations Driven by Space-time White Noise
نویسنده
چکیده
We prove existence, uniqueness and HH older continuity of a stochastic process satisfying a one dimensional wave equation driven by space-time white noise. Then we discuss a barrier problem for these stochastic wave equations in the case where we have only the stochastic term forcing the equation and where we have zero initial conditions. In a barrier problem we ask for the probability that the wave exceeds a given level. Both problems are treated rst on the whole real line and then on a nite interval with Dirichlet boundary conditions at the endpoints. Finally we give a remark on the wave equation in higher dimensions.
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