A Method for Solving a Stochastic Differential Equation : An Application to the Kinetic Ising Model with the External Noise

概要

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In this paper a new method for solving stochastic differential equations (SDE) is developed. This method, which will be named "the method of the asymptotic iteration" (MAI) , consists of two main procedures. The first is the derivation of the formal solutions of the moment equations transformed into the integral equations by iteration. The second is the selection of the terms by asymptotic evaluation and the resummation of them to derive the closed expressions for the moments. MAI is applied to the kinetic Ising model with an additive external noise. When the magnitude of noise is sufficiently small, MAI gives the same results as those of the Ω-expansion method. However, in the case where the initial state is just on the unstable point, MAI is found to be effective, while the Ω-expansion method breaks down.
理論物理学刊行会の論文
1980-10-25