Abstract.
We study nonlinear wave and heat equations on ℝd driven by a spatially homogeneous Wiener process. For the wave equation we consider the cases of d = 1, 2, 3. The heat equation is considered on an arbitrary ℝd-space. We give necessary and sufficient conditions for the existence of a function-valued solution in terms of the covariance kernel of the noise.
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Received: 1 April 1998 / Revised version: 23 June 1999 / Published online: 7 February 2000
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Peszat, S., Zabczyk, J. Nonlinear stochastic wave and heat equations. Probab Theory Relat Fields 116, 421–443 (2000). https://doi.org/10.1007/s004400050257
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DOI: https://doi.org/10.1007/s004400050257