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Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions

Annika Lang (Institutionen för matematiska vetenskaper, Tillämpad matematik och statistik) ; Andreas Petersson (Institutionen för matematiska vetenskaper, Tillämpad matematik och statistik) ; Andreas Thalhammer

The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. The purpose of this article is to discuss this property for approximations of infinite-dimensional stochastic differential equations and give necessary and sufficient conditions that ensure mean-square stability of the considered finite-dimensional approximations. Stability properties of typical discretization schemes such as combinations of spectral Galerkin, finite element, Euler-Maruyama, Milstein, Crank-Nicolson, and forward and backward Euler methods are characterized. Furthermore, results on their relationship to stability properties of the analytical solutions are provided. Simulations of the stochastic heat equation confirm the theory.

Nyckelord: Asymptotic mean-square stability, numerical approximations of stochastic differential equations, linear stochastic partial differential equations, Lévy processes, rational approximations, Galerkin methods, spectral methods, finite element methods, Euler–Maruyama scheme, Milstein scheme.

arXiv:1702.07700 [math.NA]

Denna post skapades 2017-04-10.
CPL Pubid: 248812


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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, Tillämpad matematik och statistikInstitutionen för matematiska vetenskaper, Tillämpad matematik och statistik (GU)


Sannolikhetsteori och statistik

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