Euler Method For Two Types Of Fractional Stochastic Diferential Equations

In recent decades, many scholars at home and abroad studied the modelof fractional diferential equations and stochastic diferential equations deeplyand has made the rich achievements. With the advancement of current scienceand technology, the model of fractional stochastic diferential equations has beenwidely applied in practical problems. However, little study has been carried onthis type equation. Therefore, it has important theory meaning and practice valueto study the fractional stochastic diferential equations. Convergence and stabilityof Euler method for the two types of fractional stochastic diferential equationsis mainly studied in this paper, the main work and results are summarized asfollows:1. Aiming at the problem of the first type of fractional stochastic diferen-tial equations, based on numerical idea of explicit Euler method for fractionaldiferential equations and stochastic diferential equations, the numerical schemeof explicit Euler method for this type equation is proposed in this paper. Thenconvergence and stability of numerical method is proved later. The results ofnumerical experiments verify the efectiveness and operability of the proposedmethod.2. Aiming at the problem of the second type of fractional stochastic difer-ential equations, based on numerical idea of implicit Euler method for fractionaldiferential equations and stochastic diferential equations, the numerical schemeof implicit Euler method for this type equation is proposed in this paper. Thenconvergence and stability of numerical method is proved later. The results ofnumerical experiments verify the efectiveness and operability of the proposedmethod.