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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
