The stochastic wave equation with fractional noise: A random field approach

[摘要] We consider the linear stochastic wave equation with spatially homogeneous Gaussian noise, which is fractional in time with index H > 1/2. We show that the necessary and sufficient condition for the existence of the solution is a relaxation of the condition obtained in Dalang (1999) [10], where the noise is white in time. Under this condition, we show that the solution is L-2(Omega)-continuous. Similar results are obtained for the heat equation. Unlike in the white noise case, the necessary and sufficient condition for the existence of the solution in the case of the heat equation is different (and more general) than the one obtained for the wave equation. (C) 2010 Elsevier B.V. All rights reserved.

[发布日期] 2010-12-01

[关键词] Stochastic wave equation;Random field solution;Spatially homogeneous Gaussian noise;Fractional Brownian motion