一类二维维纳过程加权和的增量讨论

A Discussion of the Increments of the Weighted Sum of a Class of Two-dimensional Wiener Processes

通过二维Wiener过程的有限加权和形式,利用正态分布的尾概率不等式和Borel-Cantelli引理,对推广的二维Wiener过程的有限加权和在区间[0,T]、长度为aT的子区间的增量有多大问题进行讨论,得出类似于一维Wiener过程的有限加权和增量有多大的结论,该结论可视为一维Wiener过程增量结果的非平凡推广。

The form of weighted sum of two-dimensional Wiener process is proposed in this paper,and discuss how large the increments of it over sub-intervals of length aTof the interval [0,T] by using the tail probability inequality of normal distribution and the Borel-Cantelli lemma. Similar to the conclusion of the increments of one-dimensional Wiener process,this result can be regarded as a non-trivial extension of one-dimensional problem.