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The Stochastic Wave Equation

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1962)

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.

Keywords

  • Wave Equation
  • Spatial Dimension
  • Mild Solution
  • Martingale Measure
  • Riesz Potential

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Robert C. Dalang .

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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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