in this comment: Expectation of reciprocal of a variable
I saw that BloXX said the following:
Taylor approx. may only be useful if one has sequence of random variables $X_n-\mu=O_p(a_n)$ where $a_n\to 0$. Even then uniform integrability is needed additionally if interested in the expectation.
I am curious, is there a reference for what he's saying? Say I have some random variables $X_n$ with mean $\mu$ and variance $\sigma_n^2=a_n$ with $a_n\to 0$. Then are they saying that the Taylor expansion is valid?
