Evelyn Buckwar, Rozsa Horváth-Bokor, Renate Winkler,
"Asymptotic mean-square stability of two-step methods for stochastic ordinary differential equations"
, in BIT Numerical Mathematics, Vol. 46, Nummer 2, Springer, Dordrecht, Seite(n) 261-282, 2006, ISSN: 0006-3835
Asymptotic mean-square stability of two-step methods for stochastic ordinary differential equations
Sprache des Titels:
We deal with linear multi-step methods for SDEs and study when the numerical
approximation shares asymptotic properties in the mean-square sense of the exact
solution. As in deterministic numerical analysis we use a linear time-invariant test
equation and perform a linear stability analysis. Standard approaches used either to
analyse deterministic multi-step methods or stochastic one-step methods do not carry
over to stochastic multi-step schemes. In order to obtain sufficient conditions for asymptotic mean-square stability of stochastic linear two-step-Maruyama methods we construct and apply Lyapunov-type functionals. In particular we study the asymptotic mean-square stability of stochastic counterparts of two-step Adams?Bashforth- and Adams?Moulton-methods, the Milne?Simpson method and the BDF method.