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In this paper, we obtain some results for the weak convergence of semi-implicit split-step (SISS)methods which are recently developed to solve a class of nonlinear stochastic differential equation with non-Lipschitz drift term. First, we present some moment estimates based on the actual and numerical solutions of stochastic Ginzburg-Landau equations by SISS methods. Then, we show that our theoretical results are consistent with the numerical results that are obtained by performing simulations. Finally, we present the weak convergence rate of SISS methods is approximately 1 with respect to the numerical results. [ABSTRACT FROM AUTHOR]

We study the fundamental solution of bond-pricing in the Ho-Lee stochastic interest rate model under the invariant criteria. We obtain transformations between Ho-Lee model with the corresponding linear (1+1) partial differential equation and the first Lie canonical form which is identical to the classical heat equation. These transformations help us to generate the fundamental solution for the Ho-Lee model with respect to the fundamental solution of the classical heat equation sense. Moreover, as a financial application of the Ho-Lee model, we choose the drift term from power functions and perform simulations via Milstein method. Furthermore, we obtain important results for the parameter calibration of the corresponding drift term by using the simulation results. [ABSTRACT FROM AUTHOR]