In this article we show the existence of a random-field solution to linearstochastic partial differential equations whose partial differential operatoris hyperbolic and has variable coefficients that may depend on the temporal andspatial argument. The main tools for this, pseudo-differential and Fourierintegral operators, come from microlocal analysis. The equations that we treatare second-order and higher-order strictly hyperbolic, and second-order weaklyhyperbolic with uniformly bounded coefficients in space. For the latter one weshow that a stronger assumption on the correlation measure of the random noisemight be needed. Moreover, we show that the well-known case of the stochasticwave equation can be embedded into the theory presented in this article.
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