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This talk is concerned with mean square stability of the classical stochastic theta method and the so called split-step theta method for multidimensional stochastic systems.First,we consider linear autonomous systems.Under a sufficient and necessary condition for exponential mean square stability of exact solution,it is proved that the two classes of theta methods with θ > 0.5 are exponentially mean square stable for all positive stepsizes and the methods with θ < 0.5 are stable for some small stepsizes.Then,we study stability of the methods for nonlinear non-autonomous systems.Under a coupled condition on the drift and diffusion coefficients,it is proved that the split-step theta method with θ> 0.5 still unconditionally preserves the exponential mean square stability of the underlying systems but the stochastic theta method does have this property.Finally,we consider some further extensions.