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\iteman{io-port 05982521}
\itemau{Wang, Xiaojie; Gan, Siqing}
\itemti{The improved split-step backward Euler method for stochastic differential delay equations.}
\itemso{Int. J. Comput. Math. 88, No. 11, 2359-2378 (2011).}
\itemab
The authors consider the numerical integration of stochastic differential delay equations $$ dx(t)=f(x(t),x(t-\tau(t)))dt+g(x(t),x(t-\tau(t)))dw(t) $$ with initial data $x(t)=\psi(t),\ t\in\lbrack-\tau,0].$ Here $\tau (t)\geq0,\ -\tau:=\inf\{t-\tau(t):t\geq0\}$, $x$ is a $d$-dimensional vector, $w(t)$ is an $m$-dimensional Wiener process. For the equation, they introduce a new Euler method and prove its convergence in the mean-square sense. Further, the exponential mean-square stability of the proposed method is investigated.
\itemrv{Grigori N. Milstein (Yekaterinburg)}
\itemcc{}
\itemut{split-step backward Euler method; strong convergence; one-sided Lipschitz condition; mean-square stability; stochastic differential delay equations}
\itemli{doi:10.1080/00207160.2010.538388}
\end