随机序列的最大连续子之和展望 [英] Expectation of the maximum consecutive subsequence sum of a random sequence

问题描述

下面是编程珠玑的问题第2版（第8.7）：

Here is a problem from Programming Pearls 2nd edition (Chapter 8.7):

考虑到一个真正的数字序列，它的元素均匀的范围绘制 [ - 1，1] ，什么是预期的最大连续子之和？ （如果所有的元素都是负值，最大的一笔是 0 ）

Considering a real number sequence, whose elements are drawn uniformly from the range [-1, 1], what is the expected maximum consecutive subsequence sum? (If all the elements are negative, the maximum sum is 0.)

假设序列的长度 N ，是有一个封闭的形式为预期的最大子之和 F（N）？我试着做一些模拟，但未能找到任何线索。

Assuming the length of the sequence is N, is there a closed form for the expected maximum subsequence sum f(N)? I try to do some simulation, but failed to find any clue.

感谢您的帮助。

推荐答案

这是类似于布朗运动一维，但是有一个不同寻常的分布步长。对于大的N它接近于维纳过程。

this is similar to Brownian motion in 1D, but with an unusual distribution for step sizes. for large N it approximates a Wiener process.

（不知道任何这是非常有帮助的，但如果你不知道的连接可能提供额外的地方寻找）。

(not sure any of that is very helpful, but if you're not aware of the connections it may give additional places to look).

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