A full discretization of the rough fractional linear heat equation

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