摘要
分数布朗运动(fBm)具有自相似性,它是布朗运动的推广,在很多领域有着重要的应用.就微积分教学中的广义积分,结合分数布朗运动模型(FBM)的建立,以第1类广义积分(无穷限)的形式,用离散逼近的方法,通过对核函数的改变,成功地模拟分数布朗运动.这是基于曼德尔布莱德建立的最初的分数布朗运动模型而改进的简单离散模型,此模型的精确度比原来的模型要高.在微积分教学中可以作为广义积分的应用举例.研究表明,当记忆充分大,计算就更加精确,记忆不小于5倍的时间步长时模拟才比较准确.所用到的广义积分的近似逼近方法,对广义积分教学具有启发性的指导作用,创新了积分理论教学.
Fractional Brownian motion（fBm）has self-similarity,it is the development of Brownian motion,and it has important application in many fields.The generalized integral in calculus teaching combined with the establishment of FBM model,the fB m is successfully simulated by the method of discrete approximation in the form of the first type of generalized integra（lwith infinite limit）,and by the change of kernel function.This is an improved simple discrete model based on the initial fB m model established by Mandelbrod,which is more accurate than the original model.It can be used as an example of generalized integral in calculus teaching.Studies shows that when memory is sufficiently large,the fB m is more accurate,the memory cannot be less than 5 times of the time step.The approximate approximation method of generalized integrals used in this paper is instructive to the generalized integral teaching and innovative integral theory teaching.
作者
瞿波
QU Bo(School of Sciences,Nantong University,Nantong 226019,China)
出处
《高师理科学刊》
2018年第4期45-50,共6页
Journal of Science of Teachers＇College and University
