2009/12/19 by Raluca M. Balan, Balan, Raluca, Ciprian A. Tudor +1
Economics, Econometrics and Finance · Engineering · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications
paper · doi:10.48550/arxiv.0912.3865
openalex publication_date 2009/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the linear stochastic wave equation with spatially homogenous 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 \citedalang99, when the noise is white in time. Under this condition, we show that the solution is L2(Ω)-continuous. Similar results are obtained for the heat equation. Unlike the white noise case, the necessary and sufficient condition for the existence of the solution in the case of the heat equation is \em different (and more general) than the one obtained for the wave equation.