A family of fully implicit strong Ito-Taylor numerical methods for stochastic differential equations

摘要

In this paper we design a family of fully implicit strong Ito-Taylor numerical methods for stochastic differential equations (SDE). These methods are based on the truncation of our general stochastic Ito-Taylor expansions, in which the truncation can be chosen to make our methods converge with high order. And by selecting the parameters in the methods, we can get methods with different stability. The mean-square (MS) stability of the second-order case is investigated. Numerical results are reported to show the convergence properties and the stability properties of our methods.

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