Nonlinear stochastic wave and heat equations
- Cite this article as:
- Peszat, S. & Zabczyk, J. Probab Theory Relat Fields (2000) 116: 421. doi:10.1007/s004400050257
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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.