Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 201 / 1 / b

Table of contents
- Solution b

Solution

The law of the iterated logarithm for a simple symmetric random walk states that almost surely

lim sup_{n \to \infty} \frac{∣ S _{n} ∣}{2 n l o g l o g n} = 1.

Since

2 lo g lo g n

is unbounded,

∣ S_{n} ∣/ n

exceeds every fixed

c > 0

at some finite time. Hence

T_{c} = in f {n \geq 0 : ∣ S_{n} ∣ > c n} < \infty

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version