Evelyn Buckwar, Rachel Kuske, Tony Shardlow, Salah-Eldin Mohammed,
"Weak convergence of the Euler scheme for stochastic differential delay equations"
, in LMS Journal of Computation and Mathematics, Vol. 11, London Mathematical Society, London, Seite(n) 60-99, 2008, ISSN: 1461-1570
Original Titel:
Weak convergence of the Euler scheme for stochastic differential delay equations
Sprache des Titels:
Englisch
Original Kurzfassung:
We study weak convergence of an Euler scheme for nonlinear stochastic delay differential equations (SDDEs) driven by multidimensional Brownian motion. The Euler scheme has weak order of convergence 1, as in the case of stochastic ordinary differential equations (SODEs) (i.e., without delay). The result holds for SDDEs with multiple finite fixed delays in the drift and diffusion terms. Although the set-up is non-anticipating, our approach uses the Malliavin calculus and the anticipating stochastic analysis techniques of Nualart and Pardoux.
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