Ito积分和Stratonovich积分的比较(英文)

Comparison of Ito and Stratonovich integrals

引入了It积分和Stratonovich积分的定义,介绍了计算It积分的It公式,并讨论了It积分和Stratonovich积分之间的关联公式。通过实例,运用这两种积分分别求解随机微分方程,并将结果进行了对比。最后,对它们在不同的实际应用中各自具有的优、缺点进行了讨论。

We introduce the definitions of the Ito integral and the Stratonovich integral and present the Ito formula used to calculate the Ito integral. Also, the equation, which represents the relationship between the Ito integral and the Stratonovich integral, is derived. Through examples, we solve the stochastic differential equations by applying the two kinds of integrals respectively and compare the solutions obtained from the two different methods. At the end, we investigate the advantages and disadvangtages of these two kinds of integrals in different practical applications.