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 Electronic Journal of Probability > Vol. 8 (2003) > Paper 1 open journal systems 


Some Non-Linear S.P.D.E's That Are Second Order In Time

Robert C. Dalang, Ecole Polytechnique Fédérale
Carl Mueller, University of Rochester


Abstract
We extend J.B. Walsh's theory of martingale measures in order to deal with stochastic partial differential equations that are second order in time, such as the wave equation and the beam equation, and driven by spatially homogeneous Gaussian noise. For such equations, the fundamental solution can be a distribution in the sense of Schwartz, which appears as an integrand in the reformulation of the s.p.d.e. as a stochastic integral equation. Our approach provides an alternative to the Hilbert space integrals of Hilbert-Schmidt operators. We give several examples, including the beam equation and the wave equation, with nonlinear multiplicative noise terms.


Full text: PDF

Pages: 1-21

Published on: February 3, 2003
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Electronic Journal of Probability. ISSN: 1083-6489