These notes give an overview of recent results concerning the non-linear stochastic wave equation in spatial dimensions d ≥ 1, in the case where the driving noise is Gaussian, spatially homogeneous and white in time. We mainly address issues of existence, uniqueness and Hölder—Sobolev regularity. We also present an extension of Walsh's theory of stochastic integration with respect to martingale measures that is useful for spatial dimensions d ≥ 3.
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Dalang, R.C. (2009). The Stochastic Wave Equation. In: Khoshnevisan, D., Rassoul-Agha, F. (eds) A Minicourse on Stochastic Partial Differential Equations. Lecture Notes in Mathematics, vol 1962. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85994-9_2
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