Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions
Artikel i vetenskaplig tidskrift, 2017
The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. This property is discussed for approximations of infinite-dimensional stochastic differential equations and necessary and sufficient conditions ensuring mean-square stability are given. They are applied to typical discretization schemes such as combinations of spectral Galerkin, finite element, Euler–Maruyama, Milstein, Crank–Nicolson, and forward and backward Euler methods. Furthermore, results on the relation to stability properties of corresponding analytical solutions are provided. Simulations of the stochastic heat equation illustrate the theory.
Asymptotic mean-square stability
Lévy processes
Euler–Maruyama scheme
numerical approximations of stochastic differential equations
spectral methods
linear stochastic partial differential equations
rational approximations
Galerkin methods
finite element methods
Milstein scheme
Författare
Annika Lang
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Andreas Petersson
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Andreas Thalhammer
Johannes Kepler Universität Linz (JKU)
BIT Numerical Mathematics
0006-3835 (ISSN) 1572-9125 (eISSN)
Vol. 57 4 963-990Ämneskategorier
Beräkningsmatematik
Sannolikhetsteori och statistik
DOI
10.1007/s10543-017-0684-7