Liang, Xiao2020-07-242020-07-242020-07-24http://hdl.handle.net/10393/40761http://dx.doi.org/10.20381/ruor-24988In this thesis, we study the linear stochastic heat and wave equations with zero initial conditions, driven by a Gaussian noise, which is fractional in space with Hurst index H ∈ (0, 1), and is either white in time (i.e. fractional in time with index H_0 = 1/2) or fractional in time with index H_0 > 1/2. We prove that the solution of each of these equations is continuous in law in the space C([0,T] × R) of continuous functions, with respect to the index H. This result has already been proved in the recent article [15] for the case H_0 = 1/2, and we extend it here to the case H_0 > 1/2.enstochastic heat equationstochastic wave equationweak convergencefractional noiseThesis