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Abstract
In this thesis, we present five composite Milstein methods for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. The com¬posite Milstein methods are a combination of semi-implicit and implicit Milstein meth¬ods. The criterion for choosing either the implicit or the semi-implicit method at each step of the numerical solution is given. The stability and convergence properties of the proposed methods are analyzed for the corresponding linear test equation. It is shown that three of the proposed methods converge to the exact solution in Ito sense while the other two converge to the exact solution in Stratonovich sense. In addition, the stability properties of our methods are found to be superior to those of the Milstein and the composite Euler methods. The convergence properties for thenonlinear case are shown numerically to be the same as the linear case. Hence, the proposed methods arc a good canrlirlFltc for the solution of stiff SDEs.