# proofs of stochastic boundedness

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?

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