# Law of Large Numbers - Rate of convergence

1. Feb 9, 2010

### Apteronotus

What is the rate of convergence of the law of large numbers?

ex.
if
$$lim_{n \rightarrow \infty} \frac{1}{n} \sum Z_n = \mu$$

1. can we say that the sum converges to $$\mu$$ as $$n^\alpha$$ for some $$\alpha\in \Re$$?

2. If so, what is the value of $$\alpha$$?

Thanks,

2. Feb 9, 2010

### mathman

It depends very much on the distribution functions of the random variables involved.

3. Feb 24, 2010

### EnumaElish

This paper has some results without proofs.

4. Feb 25, 2010