Evelyn Buckwar, Renate Winkler,
"Multistep methods for SDEs and their application to problems with small noise"
, in SIAM Journal on Numerical Analysis, Vol. 44, Nummer 2, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Seite(n) 779-803, 2006, ISSN: 0036-1429
Multistep methods for SDEs and their application to problems with small noise
Sprache des Titels:
In this article the numerical approximation of solutions of Itô stochastic differential equations is considered, in particular for equations with a small parameter $\epsilon$ in the noise coefficient. We construct stochastic linear multistep methods and develop the fundamental numerical analysis concerning their mean-square consistency, numerical stability in the mean-square sense and mean-square convergence. For the special case of two-step Maruyama schemes we derive conditions guaranteeing their mean-square consistency. Further, for the small noise case we obtain expansions of the local error in terms of the step size and the small parameter $\epsilon$. Simulation results using several explicit and implicit stochastic linear $k$-step schemes, $k=1,\;2$, illustrate the theoretical findings.
Sprache der Kurzfassung:
SIAM Journal on Numerical Analysis
Society for Industrial and Applied Mathematics (SIAM), Philadelphia