一类带乘性噪声随机分数阶微分方程Euler方法的弱收敛性与弱稳定性  

WEAK CONVERGENCE AND WEAK STABILITY OF EULER METHOD FOR A CLASS OF STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATION WITH MULTIPLICATIVE NOISE

作　　者：毛文亭 王文强[1] 林伟贤[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《计算数学》2016年第4期442-452,共11页Mathematica Numerica Sinica

基　　金：国家自然科学基金(11571373;11671343);湖南省教育厅重点项目(14A146)资助项目

摘　　要：本文主要在带加性噪声随机分数阶微分方程的基础上,研究了一类更为困难的带乘性噪声随机分数阶微分方程Euler方法的弱收敛性与弱稳定性,并得到了类似的结论.首先构造了数值求解带乘性噪声随机分数阶微分方程的Euler方法,然后证明当分数阶α满足0<α<1/2时,该方法是1/2-α阶弱收敛的和弱稳定的,文末数值试验的结果验证了理论结果的正确性.Based on the stochastic fractional differential equation with additive noise, this paper studied the weak convergence and weak stability of Euler method for a class of stochastic frac- tional differential equation with multiplicative noise, and a similar conclusion is obtained as well. Firstly, the Euler method was constructed to solve the stochastic fractional differential 1/2 -α-order equation with multiplicative noise, and then it was proved that the method was 1 Finally, weak convergence and weak stability when the fractional order a satisfy 0 〈 α 〈1/2. one numerical example is given. The theoretical results are also confirmed by a numerical experiment.

关 键 词：带乘性噪声随机分数阶微分方程 EULER方法 弱收敛性 弱稳定性 

分 类 号：O241.8[理学—计算数学]