Weak convergence of the Euler scheme for stochastic differential delay equations
Evelyn Buckwar, Rachel Kuske, Salah-Eldin Mohammed and Tony Shardlow
Abstract: We study weak convergence of an Euler scheme for non-linear
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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