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Convergence and stability of the semi-implicit Euler method for linear stochastic delay integro-differential equations. (English) Zbl 1115.65007
As explicit solutions can rarely be obtained for stochastic delay integro-differential equations (SDIDEs), it is useful to develop numerical approximations, even in the linear case. It is proved in this paper that a semi-implicit Euler method is convergent with strong order $p=0.5$. Under a simple condition on the coefficients, the Lyapunov function method proves that the zero solution of the SDIDE is asymptotic mean square stable. The same is true for the semi-implicit Euler method with suitable time step. Numerical experiments are presented.

65C30Stochastic differential and integral equations
60H20Stochastic integral equations
60H35Computational methods for stochastic equations
45R05Random integral equations
65R20Integral equations (numerical methods)
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