I'm looking at some statistical literature and trying to compare the results given there in probabilistic big-Oh notation with statements I'm more familiar with.


In particular, I'm trying to interpret statements of the form
$$
\|\Sigma\_{n(p)} - \Sigma \| = O\_P\left( \frac{\log p}{n(p)}\right).
$$
As far as i can tell from the rather terse wikipedia page on $o\_p$ notation, this means that there is some constant $C$ that is independent of $p$ for which
$$
\lim\_{p \rightarrow \infty} \mathbb{P}\left( \|\Sigma\_{n(p)} - \Sigma \| > C \frac{\log p}{n(p)}\right) = 0.
$$


Is that correct?



proofs of stochastic boundedness
The problem is that there are no universally agreed upon notations. Maybe [this](http://arxiv.org/abs/1108.3924) will help.


