Abstract
We study a full discretization scheme for the stochastic linear heat equationwhen B˙ is a very rough space-time fractional noise. The discretization procedure is divised into three steps: (i) regularization of the noise through a mollifying-type approach; (ii) discretization of the (smoothened) noise as a finite sum of Gaussian variables over rectangles in [0,1]×R; (iii) discretization of the heat operator on the (non-compact) domain [0,1]×R, along the principles of Galerkin finite elements method. We establish the convergence of the resulting approximation to , which, in such a specific rough framework, can only hold in a space of distributions. We also provide some partial simulations of the algorithm.
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