Convergence Rate of EM Scheme for SDDEs

Details Convergence Rate of EM Scheme for SDDEs Convergence Rate of EM Scheme for SDDEs

2011-11-17

arxiv.org/abs/1111.4130v1

Mathematics

Probability

Page 13

Scientific paper

In this paper we investigate the convergence rate of Euler-Maruyama scheme for a class of stochastic differential delay equations, where the corresponding coefficients may be highly nonlinear with respect to the delay variables. In particular, we reveal that the convergence rate of Euler-Maruyama scheme is 1/2$ for the Brownian motion case, while show that it is best to use the mean-square convergence for the pure jump case, and that the order of mean-square convergence is close to 1/2.

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