Mean-square stability analysis of SPDE approximations
Sprache des Vortragstitels:
Winter School on Numerics for Stochastic Partial Differential Equations and their Applications, Special Semester Special Semester on Computational Methods in Science and Engineering
Sprache des Tagungstitel:
We examine the asymptotic mean-square stability properties of the zero solution of SPDE approximations. For this we consider fully discrete one-step approximation schemes applied to linear SPDEs with multiplicative noise driven by square-integrable martingales. Since the (standard) finite-dimensional approach to qualitatively analyse the stability properties of numerical approximations of SDEs is not suitable for fine spatial refinement levels due to the high computational cost, we develop tools that allow us to investigate the mean-square stability properties of the zero solution of the fully discrete scheme on an operator-valued level.