Weak convergence of the Euler scheme for stochastic differential delay equations

Reference:

Buckwar, E., Kuske, R., Mohammed, S.-E. and Shardlow, T., 2008. Weak convergence of the Euler scheme for stochastic differential delay equations. London Mathematical Society Journal of Computation and Mathematics, 11, pp. 60-99.

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Official URL:

http://dx.doi.org/10.1112/S146115700000053X

Abstract

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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